Nothing
R/NaiveEstimation.R
In GDILM.ME: Spatial Modeling of Infectious Diseases with Co-Variate Error
Defines functions
NaiveEstimation
Documented in
NaiveEstimation
#' Estimating parameters along with corresponding variances based on Naive model.
#'
#' @param ITER The number of simulation runs
#' @param MHiteration The number of iterations in Metropolis–Hastings algorithm
#' @param eps Stopping value for MCECM algorithm
#' @param d distance between cells
#' @param nSample number of sample in each cell
#' @param mm Number of areas.
#' @param time Maximum time.
#' @param MuxStar0 Mean of unobserved areal level covariates.
#' @param MuxInd0 Mean of unobserved individual level covariates.
#' @param SigmaxStar0 Variance of unobserved areal level covariates.
#' @param SigmaxInd0 Variance of unobserved individual level covariates.
#' @param Sigmav0 Variance of areal level measurement error variable.
#' @param Sigmaw0 Variance of individual level measurement error variable.
#' @param lambda0 Spatial dependency parameter.
#' @param sigma0 Over dispersion parameter.
#' @param delta0 The spatial parameter.
#' @param alpha0 Initial value for intercept.
#' @param beta10 Initial value for coefficient of observed individual level covariates.
#' @param beta20 Initial value for coefficient of observed areal level covariates.
#' @param beta30 Initial value for coefficient of unobserved individual level covariates.
#' @param beta40 Initial value for coefficient of unobserved areal level covariates.
#' @param InfPeriod The infectious period length.
#' @param g grid dimension
#'
#' @return The results of the function
#'
#' @export
#'
#' @importFrom mvtnorm dmvnorm
#' @importFrom MASS mvrnorm
#' @importFrom numDeriv hessian
#' @importFrom stats optim
#' @importFrom stats rnorm
#' @importFrom stats dnorm
#' @importFrom stats runif
#' @importFrom ngspatial adjacency.matrix
#' @importFrom corpcor make.positive.definite
#' @importFrom psych tr
#'
#'
#' @examples NaiveEstimation(1,5,0.05,2,4,4,20,0,0,1,1,0.3,0.3,0.5,0.5,2.5,0,1,
#' 1,1,1,3,2)
#'
#'
NaiveEstimation=function(ITER,MHiteration,eps,d,nSample,mm,time,MuxStar0,MuxInd0,SigmaxStar0,SigmaxInd0,Sigmav0,Sigmaw0,lambda0,sigma0,delta0,alpha0,beta10,beta20,beta30,beta40,InfPeriod,g){
############################a######Generate Data############################
nn=MHiteration
N = rep(nSample,(g^2))
n=sum(N)
i=n
NaivSimPAR=matrix(0,ITER,8)
NaivSimVarPar=matrix(0,ITER,6)
NaivCSimVarPar=matrix(0,ITER,6)
NaivSimInfPar=matrix(0,ITER,6)
NaivSimVarSpatial=matrix(0,ITER,2)
NaivSimPos=list()
lambda=rep(InfPeriod,n) #########ifected period##############
I=diag(mm)
A1=adjacency.matrix(g, g)
A2=colSums(A1)
D=-A1
diag(D)=A2
###############################Covaraites without measurement error#######################
cov1=rnorm(n,0,1)
cov2=rnorm(mm,0,1)
#####################infected time #####################
D1=c()
for(mmm in 1:mm){
D1[mmm]=sample(N[mmm],1,replace=F)
}
D1
tau1=list()
for(i in 1:mm){
tau1[[i]]=rep(0,N[i])
tau1[[i]][D1[i]]=1
}
tau=unlist(tau1)
Nlabel1=list()
for(i in 1:mm){
Nlabel1[[i]]=rep(i,N[i])
}
Nlabel=unlist(Nlabel1)
Newlabel=matrix(0,n,mm)
for(mmm in 1:mm){
Newlabel[,mmm]=rep(D[,mmm],N)
}
CovXStar1=rnorm(mm, MuxStar0, sqrt(SigmaxStar0))
CovX=rnorm(n, MuxInd0, sqrt(SigmaxInd0))
data=array(0,c(n,2,ITER))
for (iter in 1:ITER) {
xx = c(rep(0,nSample*g*g))
for (gg in 1:g) {
x=matrix(0,nSample,g)
for(i in 1:g){
x[,i]=runif(nSample,d*(gg-1),d*gg)
}
v=nSample*gg*g
xx[1:v] = c(x)
}
X=c(xx)
yy = c(rep(0,nSample*g*g))
for (gg in 1:g) {
y=matrix(0,nSample,gg)
for(i in 1:gg){
y[,i]=runif(nSample,d*(i-1),d*i)
}
z=nSample*gg*g
yy[1:z] = c(y)
}
Y = c(yy)
data[,,iter]=cbind(X,Y)
}
############################## f_y|x,xStar,u###############################
Fy1=function(IndLe,AreLe,RaE,alpha1,beta1,beta2,beta3,beta4,delta,time,tau,mm,lambda){
fy1=array(0,c(n,time,mm))
for(i in 1:n){
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob1=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*IndLe[i]+beta4*AreLe[mmm]+RaE[mmm])*dx)
fy1[i,t,mmm]=(1-prob1)
}
if (tau[i]==(t+1)){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob1=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*IndLe[i]+beta4*AreLe[mmm]+RaE[mmm])*dx)
fy1[i,t,mmm]=prob1
}
}
}
}
}
PP=c()
H=list()
fy2=c()
for(mmm in 1:mm){
for(i in 1:n){
PP[i]=round(prod(fy1[i,,mmm][fy1[i,,mmm]>0]),10)
}
H[[mmm]]=which(PP!=1)
fy2[mmm]=prod(PP[H[[mmm]]][PP[H[[mmm]]]>0])
}
return(fy2)
}
##############################################################################################
fRanE=function(RaE,mmm,lambda1,sigma1,D){
Nh=-D[,mmm]*RaE
dnorm(RaE[mmm],lambda1/(1-lambda1+D[mmm,mmm]*lambda1)*sum(Nh[-mmm]),sqrt(1/(sigma1^2*(1-lambda1+D[mmm,mmm]*lambda1))), log = FALSE)
}
#################Sum h(z-z_{I}) #######################
SumH=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH1[j]=Di[i,j]^(-delta)
}
}
}
SumH1=replace(SumH1,is.infinite(SumH1),0)
SumH2=sum(SumH1)
SumH3=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH2
return(SumH3)
}
#################Sum h(z-z_{I})log(d_{ij}) #######################
SumHnew1=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH4=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH4[j]=Di[i,j]^(-delta)*(log(Di[i,j]))
}
}
}
SumH4=replace(SumH4,is.infinite(SumH4),0)
SumH5=sum(SumH4)
SumH6=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH5
return(SumH6)
}
#################Sum h(z-z_{I})(log(d_{ij}))^2 #######################
SumHnew2=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH7=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH7[j]=Di[i,j]^(-delta)*(log(Di[i,j]))^2
}
}
}
SumH7=replace(SumH7,is.infinite(SumH7),0)
SumH8=sum(SumH7)
SumH9=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH8
return(SumH9)
}
E.sigma.first=function(Pos,D,lambda1){
d1=c()
for(L in 1:nn){
d1[L]=as.numeric(t(Pos[L,(mm+1):(2*mm)])%*%(lambda1*D+(1-lambda1)*I)%*%Pos[L,(mm+1):(2*mm)])
}
SMeansigma1=mean(d1)
return(SMeansigma1)
}
E.lambda1.first=function(Pos,D){
d2=c()
for(L in 1:nn){
d2[L]= as.numeric(t(Pos[L,(mm+1):(2*mm)])%*%(D-I)%*%Pos[L,(mm+1):(2*mm)])
}
SMeanlambda11=mean(d2)
return(SMeanlambda11)
}
######################################### Expectation #######################
mean1=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMean1=mean(d1)
return(SMean1)
}
meanXstar1=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanXstar1=mean(d1)
return(SMeanXstar1)
}
meanX1=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanX1=mean(d1)
return(SMeanX1)
}
meanXstar3=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,mmm]^2*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanXstar3=mean(d1)
return(SMeanXstar3)
}
meanX3=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,(2*mm+i)]^2*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanX3=mean(d1)
return(SMeanX3)
}
###############################################################
mean2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,(mmm+mm)])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean2=0}
if(prob11!=0){
SMean2=(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMean2)
}
meanXstar2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXstar2=0}
if(prob11!=0){
SMeanXstar2=Pos[L,mmm]*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanXstar2)
}
meanX2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX2=0}
if(prob11!=0){
SMeanX2=Pos[L,(2*mm+i)]*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanX2)
}
meanXstar4=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXstar4=0}
if(prob11!=0){
SMeanXstar4=Pos[L,mmm]^2*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanXstar4)
}
meanX4=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX4=0}
if(prob11!=0){
SMeanX4=Pos[L,(2*mm+i)]^2*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanX4)
}
####################################################################
mean3=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean3=0}
if(prob11!=0){
SMean3=(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]++2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean3)
}
meanXstar5=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean5=0}
if(prob11!=0){
SMean5=Pos[L,mmm]^2*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean5)
}
meanX5=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean5=0}
if(prob11!=0){
SMean5=Pos[L,(2*mm+i)]^2*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean5)
}
############################################################################################################################
estfunNaiv=function(Nlabel,phi,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda){
##################M-H###############################
nn=MHiteration
AreLe0=vv
IndLe0=ww
mu=rep(0,mm)
Sigma11=sigma1^2*solve((lambda1*D+(1-lambda1)*I))
Sigma1 = make.positive.definite(Sigma11, tol = 1e-3)
RaE0=mvrnorm(1, mu, Sigma11, tol = 1e-6)
First=c(AreLe0,RaE0,IndLe0)
Pos=matrix(0,nrow=nn+1,ncol=((2*mm)+n))
Pos[1,]=First
MPHprob3=matrix(0,nn,n)
Uni3=matrix(0,nn,n)
MPHprob1=matrix(0,nn,mm)
Uni1=matrix(0,nn,mm)
MPHprob2=c()
Uni2=c()
for (L in 2:nn){
AreLe=vv
IndLe=ww
RaE=mvrnorm(1, mu, Sigma11, tol = 1e-6)
Pos[L,(2*mm+1):(2*mm+n)]=IndLe
Pos[L,1:mm]=AreLe
Area_sec3=Fy1(Pos[L-1,(2*mm+1):(2*mm+n)],Pos[L-1,1:mm],RaE,alpha1,beta1,beta2,beta3,beta4,delta,time,tau,mm,lambda)
Area_sec4=Fy1(Pos[L-1,(2*mm+1):(2*mm+n)],Pos[L-1,1:mm],Pos[L-1,(mm+1):(2*mm)],alpha1,beta1,beta2,beta3,beta4,delta,time,tau,mm,lambda)
Uni2[L]=runif(1,0,1)
MPHprob2[L]=min(1,prod(Area_sec3/Area_sec4))
if(Uni2[L]<MPHprob2[L]){
Pos[L,(mm+1):(2*mm)]=RaE
}
if(Uni2[L]>=MPHprob2[L]){
Pos[L,(mm+1):(2*mm)]=Pos[L-1,(mm+1):(2*mm)]
}
}
######################################## alpha #######################################
NewtonAlpha=function(Newalpha1){
A1=rep(0,time)
for(t in 1:time){
A2=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
A2[i]=-as.numeric(SumH(Nlabel,Di,Newalpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
A1[t]=sum(A2)
}
SusA1=sum(A1)
###################### infectious period ###################
A3=rep(0,time)
for(t in 1:time){
A4=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SA4=c()
for(L in 1:nn){
SA4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
A4[i]=mean(SA4)*SumH(Nlabel,Di,Newalpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
A3[t]=sum(A4)
}
InfA3=sum(A3,na.rm=T)
EndA3=SusA1+InfA3
######################### Second Der...########################
##################### infectious period ###################
A5=rep(0,time)
for(t in 1:time){
A6=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SA6=c()
for(L in 1:nn){
SA6[L]=-mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
A6[i]=mean(SA6)*SumH(Nlabel,Di,Newalpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2
}
}
}
}
A5[t]=sum(A6)
}
InfA5=sum(A5,na.rm=T)
EndA5=EndA3+InfA5
EstAlpha1=Newalpha1-EndA3/EndA5
diffAlpha=EstAlpha1-Newalpha1
result=list(Newalpha1=EstAlpha1,diffAlpha=diffAlpha)
result
}
talpha=1
Nalpha0=NewtonAlpha(alpha1)
diffAlpha=Nalpha0$diffAlpha
Newalpha1=Nalpha0$Newalpha1
EstAlpha=Newalpha1
#################################beta1##################################
NewtonBeat1=function(Newbeta1){
Beta11=rep(0,time)
for(t in 1:time){
Beta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta12[i]=-cov1[i]*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta11[t]=sum(Beta12)
}
SusBeta11=sum(Beta11)
###################### infectious period ###################
Beta13=rep(0,time)
for(t in 1:time){
Beta14=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB4=c()
for(L in 1:nn){
SB4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta14[i]=cov1[i]*mean(SB4)*SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
Beta13[t]=sum(Beta14)
}
InfBeta13=sum(Beta13,na.rm=T)
EndBeta13=SusBeta11+InfBeta13
######################### Second Der...########################
##################### infectious period ###################
Beta112=rep(0,time)
for(t in 1:time){
Beta122=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta122[i]=-cov1[i]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta112[t]=sum(Beta122)
}
SusBeta112=sum(Beta112)
Beta15=rep(0,time)
for(t in 1:time){
Beta16=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB6=c()
for(L in 1:nn){
SB6[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SB8=c()
for(L in 1:nn){
SB8[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta16[i]=cov1[i]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)*mean(SB6))-cov1[i]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(SB8))
}
}
}
}
Beta15[t]=sum(Beta16)
}
InfBeta15=sum(Beta15,na.rm=T)
EndBeta15=SusBeta112+InfBeta15
EstBeta1New1=Newbeta1-EndBeta13/EndBeta15
diffBeat1=EstBeta1New1-Newbeta1
result=list(Newbeta1=EstBeta1New1,diffBeat1=diffBeat1)
result
}
if(is.na(EstAlpha)){
EstBeta1=NA
}
if(!is.na(EstAlpha)){
tbeta1=1
Nbeta10=NewtonBeat1(beta1)
diffBeat1=Nbeta10$diffBeat1
Newbeta1=Nbeta10$Newbeta1
EstBeta1=Newbeta1
}
#################################beta2##################################
NewtonBeat2=function(Newbeta2){
Beta21=rep(0,time)
for(t in 1:time){
Beta22=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta22[i]=-cov2[mmm]*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta21[t]=sum(Beta22)
}
SusBeta21=sum(Beta21)
###################### infectious period ###################
Beta23=rep(0,time)
for(t in 1:time){
Beta24=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB10=c()
for(L in 1:nn){
SB10[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta24[i]=cov2[mmm]*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean(SB10))
}
}
}
}
Beta23[t]=sum(Beta24)
}
InfBeta23=sum(Beta23,na.rm=T)
EndBeta23=SusBeta21+InfBeta23
######################### Second Der...########################
##################### infectious period ###################
Beta212=rep(0,time)
for(t in 1:time){
Beta222=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta222[i]=-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta212[t]=sum(Beta222)
}
SusBeta212=sum(Beta212)
Beta25=rep(0,time)
for(t in 1:time){
Beta26=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB12=c()
for(L in 1:nn){
SB12[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SB14=c()
for(L in 1:nn){
SB14[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta26[i]=cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean(SB12))-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)^2*mean(SB14))
}
}
}
}
Beta25[t]=sum(Beta26)
}
InfBeta25=sum(Beta25,na.rm=T)
EndBeta25=SusBeta212+InfBeta25
##################################################################
EstBeta2New1=Newbeta2-EndBeta23/EndBeta25
diffBeat2=EstBeta2New1-Newbeta2
result=list(Newbeta2=EstBeta2New1,diffBeat2=diffBeat2)
result
}
if(is.na(EstBeta1)){
EstBeta2=NA
}
if(!is.na(EstBeta1)){
tbeta2=1
Nbeta20=NewtonBeat2(beta2)
diffBeat2=Nbeta20$diffBeat2
Newbeta2=Nbeta20$Newbeta2
EstBeta2=Newbeta2
}
if(is.na(EstBeta2)){
EstBeta3=NA
}
if(!is.na(EstBeta2)){
#################################beta4##################################
Beta31=rep(0,time)
for(t in 1:time){
Beta32=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta32[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanX1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta31[t]=sum(Beta32)
}
SusBeta31=sum(Beta31)
###################### infectious period ###################
Beta33=rep(0,time)
for(t in 1:time){
Beta34=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB13=c()
for(L in 1:nn){
SXB13[L]=meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta34[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB13))
}
}
}
}
Beta33[t]=sum(Beta34)
}
InfBeta33=sum(Beta33,na.rm=T)
EndBeta33=SusBeta31+InfBeta33
######################### Second Der...########################
##################### infectious period ###################
Beta312=rep(0,time)
for(t in 1:time){
Beta322=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta322[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanX3(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta312[t]=sum(Beta322)
}
SusBeta312=sum(Beta312)
Beta35=rep(0,time)
for(t in 1:time){
Beta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB23=c()
for(L in 1:nn){
SXB23[L]=meanX4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SXB53=c()
for(L in 1:nn){
SXB53[L]=meanX5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta36[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB23))-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)^2*mean(SXB53))
}
}
}
}
Beta35[t]=sum(Beta36)
}
InfBeta35=sum(Beta35,na.rm=T)
EndBeta35=SusBeta312+InfBeta35
EstBeta3=beta3-EndBeta33/EndBeta35
EstBeta3
}
##################################################################
if(is.na(EstBeta3)){
EstBeta4=NA
}
if(!is.na(EstBeta3)){
#################################beta4##################################
Beta41=rep(0,time)
for(t in 1:time){
Beta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta42[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanXstar1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta41[t]=sum(Beta42)
}
SusBeta41=sum(Beta41)
###################### infectious period ###################
Beta43=rep(0,time)
for(t in 1:time){
Beta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB2=c()
for(L in 1:nn){
SXB2[L]=meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta44[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB2))
}
}
}
}
Beta43[t]=sum(Beta44)
}
InfBeta43=sum(Beta43,na.rm=T)
EndBeta43=SusBeta41+InfBeta43
######################### Second Der...########################
##################### infectious period ###################
Beta412=rep(0,time)
for(t in 1:time){
Beta422=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta422[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanXstar3(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta412[t]=sum(Beta422)
}
SusBeta412=sum(Beta412)
Beta45=rep(0,time)
for(t in 1:time){
Beta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB4=c()
for(L in 1:nn){
SXB4[L]=meanXstar4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SXB5=c()
for(L in 1:nn){
SXB5[L]=meanXstar5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta46[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB4))-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)^2*mean(SXB5))
}
}
}
}
Beta45[t]=sum(Beta46)
}
InfBeta45=sum(Beta45,na.rm=T)
EndBeta45=SusBeta412+InfBeta45
EstBeta4=beta4-EndBeta43/EndBeta45
EstBeta4
}
##################################################################
################################# Delta #############################
################## susceptible period ####################
NewtonDelta=function(NewDelta){
S8=rep(0,time)
for(t in 1:time){
S7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
S7[i]=as.numeric(SumHnew1(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
S8[t]=sum(S7)
}
SusNew8=sum(S8)
###################### infectious period ###################
I10=rep(0,time)
for(t in 1:time){
I9=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXD2=c()
for(L in 1:nn){
SXD2[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
I9[i]=-as.numeric(SumHnew1(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean(SXD2))
}
}
}
}
I10[t]=sum(I9)
}
InfeNew10=sum(I10,na.rm=T)
EndNew10=SusNew8+InfeNew10
######################### Second Der...########################
S10=rep(0,time)
for(t in 1:time){
S9=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
S9[i]=-as.numeric(SumHnew2(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
S10[t]=sum(S9)
}
SusNew10=sum(S10)
###################### infectious period ###################
I12=rep(0,time)
for(t in 1:time){
I11=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXD4=c()
for(L in 1:nn){
SXD4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SXD6=c()
for(L in 1:nn){
SXD6[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
I11[i]=as.numeric(SumHnew2(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean(SXD4))-as.numeric(SumHnew1(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)^2*mean(SXD6))
}
}
}
}
I12[t]=sum(I11)
}
InfeNew12=sum(I12,na.rm=T)
EndNew12=SusNew10+InfeNew12
Estdelta1=NewDelta-EndNew10/EndNew12
diffDelta=Estdelta1-NewDelta
result=list(NewDelta=Estdelta1,diffDelta=diffDelta)
result
}
if(is.na(EstBeta4)){
Estdelta=NA
}
if(!is.na(EstBeta4)){
tdelta=1
Ndelta0=NewtonDelta(delta)
diffDelta=Ndelta0$diffDelta
NewDelta=Ndelta0$NewDelta
Estdelta=NewDelta
}
if(is.na(Estdelta)){
HatSigmmaU=NA
EstGammau=NA
MuxStarHat=NA
SigmaxStarHat=NA
MuxHat=NA
SigmaIndHat=NA
}
if(!is.na(Estdelta)){
##################################### Sigma_U #####################
##################################### Sigma_U #####################
##################################### Sigma_U #####################
##################################### Sigma_U ####################
Loglik11=function(par){
lambda1=par[[1]]
sigma1=par[[2]]
Log1=c()
for(L in 1:nn){
Log1[L]=dmvnorm(Pos[L,(mm+1):(2*mm)], rep(0,mm),sigma1^2*solve((lambda1*D+(1-lambda1)*I)), log = T)
}
LLL=-mean(Log1)
return(LLL)
}
init =c(lambda1,sigma1)
ml <- optim( init,Loglik11)
EstU1=ml$par
HatSigmmaU=EstU1[2]
EstGammau=EstU1[1]
#############################################################
#############################################################
MuxHat=0
SigmaIndHat=0
MuxStarHat=0
SigmaxStarHat=0
}
#############################################################
result=list(Pos1=Pos,beta1=EstBeta1,beta2=EstBeta2,beta3=EstBeta3,beta4=EstBeta4,alpha1=EstAlpha,delta=Estdelta,sigma1=HatSigmmaU,lambda1=EstGammau)
result
}
LogNaiv=function(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda){
nn=MHiteration
SumH=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH1[j]=Di[i,j]^(-delta)
}
}
}
SumH1=replace(SumH1,is.infinite(SumH1),0)
SumH2=sum(SumH1)
SumH3=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH2
return(SumH3)
}
mean1L=function(Pos1,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=exp(beta3*Pos1[L,(2*mm+i)]+beta4*Pos1[L,mmm]+Pos1[L,mmm+mm])
}
SMean1=mean(d1)
return(SMean1)
}
mean2L=function(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos1[L,(2*mm+i)]+beta4*Pos1[L,mmm]+Pos1[L,(mmm+mm)])*dx)
if(prob11==0){SMean2=0}
if(prob11!=0){
SMean2=log(prob11)
}
return(SMean2)
}
A1=rep(0,time)
for(t in 1:time){
A2=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
A2[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1L(Pos1,beta3,beta4,mmm,i))
}
}
}
}
A1[t]=sum(A2)
}
SusA1=sum(A1)
###################### infectious period ###################
A3=rep(0,time)
for(t in 1:time){
A4=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SA4=c()
for(L in 1:nn){
SA4[L]=mean2L(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
A4[i]=mean(SA4)
}
}
}
}
A3[t]=sum(A4)
}
InfA3=sum(A3,na.rm=T)
EndA3L=SusA1+InfA3
Log1=c()
for(L in 1:nn){
Log1[L]=dmvnorm(Pos1[L,(mm+1):(2*mm)], rep(0,mm), sigma1^2*solve((lambda1*D+(1-lambda1)*I)), log = T)
}
LLL=mean(Log1)
loglik1=LLL+EndA3L
return(loglik1)
}
##################################################################################
ObsInfNaiv=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,lambda){
nn=MHiteration
################################################################################################################
################################################################################################################
################################################################################################################
##################################################### Inf alpha ###########################################################
##################################################### Cov ###########################################################
alphaS=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
alphaS1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
alphaS1[t]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
alphaS[i,L]=sum(alphaS1)
}
}
alphaI=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
alphaI1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
alphaI1[t]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
alphaI[i,L]=sum(alphaI1)
}
}
alphaIS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
alphaIS[i,L]=alphaS[i,L]+alphaI[i,L]
}
}
SecondAlpha=c()
for(i in 1:n){
SecondAlpha[i]=mean(alphaIS[i,]^2)
}
FirstAlpha=c()
for(i in 1:n){
FirstAlpha[i]=mean(alphaIS[i,])^2
}
MAlpha=c()
for(i in 1:n){
MAlpha[i]=mean(alphaIS[i,])
}
##################################################################################
IA5=rep(0,time)
for(t in 1:time){
IA6=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISA6=c()
for(L in 1:nn){
ISA6[L]=-mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IA6[i]=mean(ISA6)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2
}
}
}
}
IA5[t]=sum(IA6)
}
IInfA5=sum(IA5,na.rm=T)
IEndA5=IInfA5+sum(MAlpha)
######################################
InfAlpha=-IEndA5-sum(SecondAlpha)+sum(FirstAlpha)
##################################################################################################################
####################################### Info beta1 ##############################
####################################### New beta1##############################
###############################Cov#######################################
Beta1S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta1S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta1S1[t]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta1S[i,L]=sum(Beta1S1)
}
}
###################### infectious period ###################
Beta1I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta1I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta1I1[t]=cov1[i]*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
Beta1I[i,L]=sum(Beta1I1)
}
}
Beta1IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta1IS[i,L]=Beta1S[i,L]+Beta1I[i,L]
}
}
SecondBeta1=c()
for(i in 1:n){
SecondBeta1[i]=mean(Beta1IS[i,]^2)
}
FirstBeta1=c()
for(i in 1:n){
FirstBeta1[i]=mean(Beta1IS[i,])^2
}
MBeta1=c()
for(i in 1:n){
MBeta1[i]=mean(Beta1IS[i,])
}
##########################################################################################
##########################################################################################
##########################################################################################
######################### Second Der...########################
##################### infectious period ###################
IBeta112=rep(0,time)
for(t in 1:time){
IBeta122=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta122[i]=-cov1[i]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta112[t]=sum(IBeta122)
}
ISusBeta112=sum(IBeta112)
IBeta15=rep(0,time)
for(t in 1:time){
IBeta16=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISB6=c()
for(L in 1:nn){
ISB6[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISB8=c()
for(L in 1:nn){
ISB8[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta16[i]=cov1[i]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISB6))-cov1[i]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISB8))
}
}
}
}
IBeta15[t]=sum(IBeta16)
}
IInfBeta15=sum(IBeta15,na.rm=T)
IEndBeta15=ISusBeta112+IInfBeta15
######################################
InfBeta1=-IEndBeta15-sum(SecondBeta1)+sum(FirstBeta1)
###########################################################################################
####################################### Info beta2 ##############################
#######################################Cov##############################
Beta2S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta2S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta2S1[t]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta2S[i,L]=sum(Beta2S1)
}
}
###################### infectious period ###################
Beta2I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta2I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta2I1[t]=cov2[mmm]*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
Beta2I[i,L]=sum(Beta2I1)
}
}
Beta2IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta2IS[i,L]=Beta2S[i,L]+Beta2I[i,L]
}
}
SecondBeta2=c()
for(i in 1:n){
SecondBeta2[i]=mean(Beta2IS[i,]^2)
}
FirstBeta2=c()
for(i in 1:n){
FirstBeta2[i]=mean(Beta2IS[i,])^2
}
MBeta2=c()
for(i in 1:n){
MBeta2[i]=mean(Beta2IS[i,])
}
########################################################################################
########################################################################################
######################### Second Der...########################
##################### infectious period ###################
IBeta212=rep(0,time)
for(t in 1:time){
IBeta222=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta222[i]=-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta212[t]=sum(IBeta222)
}
ISusBeta212=sum(IBeta212)
IBeta25=rep(0,time)
for(t in 1:time){
IBeta26=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISB12=c()
for(L in 1:nn){
ISB12[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISB14=c()
for(L in 1:nn){
ISB14[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta26[i]=cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISB12))-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISB14))
}
}
}
}
IBeta25[t]=sum(IBeta26)
}
IInfBeta25=sum(IBeta25,na.rm=T)
IEndBeta25=ISusBeta212+IInfBeta25
######################################
InfBeta2=-IEndBeta25-sum(SecondBeta2)+sum(FirstBeta2)
###########################################################################################
####################################### Info beta3 ##############################
####################################### Cov##############################
Beta3S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta3S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta3S1[t]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta3S[i,L]=sum(Beta3S1)
}
}
###################### infectious period ###################
Beta3I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta3I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta3I1[t]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Beta3I[i,L]=sum(Beta3I1)
}
}
Beta3IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta3IS[i,L]=Beta3S[i,L]+Beta3I[i,L]
}
}
SecondBeta3=c()
for(i in 1:n){
SecondBeta3[i]=mean(Beta3IS[i,]^2)
}
FirstBeta3=c()
for(i in 1:n){
FirstBeta3[i]=mean(Beta3IS[i,])^2
}
MBeta3=c()
for(i in 1:n){
MBeta3[i]=mean(Beta3IS[i,])
}
###############################################################################################
###############################################################################################
#################################beta4##################################
##################### infectious period ###################
IBeta312=rep(0,time)
for(t in 1:time){
IBeta322=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta322[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX3(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta312[t]=sum(IBeta322)
}
ISusBeta312=sum(IBeta312)
IBeta35=rep(0,time)
for(t in 1:time){
IBeta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISXB316=c()
for(L in 1:nn){
ISXB316[L]=meanX4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISXB315=c()
for(L in 1:nn){
ISXB315[L]=meanX5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta36[i]=as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISXB316))-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISXB315))
}
}
}
}
IBeta35[t]=sum(IBeta36)
}
IInfBeta35=sum(IBeta35,na.rm=T)
IEndBeta35=ISusBeta312+IInfBeta35
######################################
InfBeta3=-IEndBeta35-sum(SecondBeta3)+sum(FirstBeta3)
###########################################################################################
###########################################################################################
####################################### Info beta4 ##############################
####################################### Cov##############################
Beta4S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta4S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta4S1[t]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta4S[i,L]=sum(Beta4S1)
}
}
###################### infectious period ###################
Beta4I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta4I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta4I1[t]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Beta4I[i,L]=sum(Beta4I1)
}
}
Beta4IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta4IS[i,L]=Beta4S[i,L]+Beta4I[i,L]
}
}
SecondBeta4=c()
for(i in 1:n){
SecondBeta4[i]=mean(Beta4IS[i,]^2)
}
FirstBeta4=c()
for(i in 1:n){
FirstBeta4[i]=mean(Beta4IS[i,])^2
}
MBeta4=c()
for(i in 1:n){
MBeta4[i]=mean(Beta4IS[i,])
}
###############################################################################################
###############################################################################################
#################################beta4##################################
##################### infectious period ###################
IBeta412=rep(0,time)
for(t in 1:time){
IBeta422=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta422[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar3(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta412[t]=sum(IBeta422)
}
ISusBeta412=sum(IBeta412)
IBeta45=rep(0,time)
for(t in 1:time){
IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISXB4=c()
for(L in 1:nn){
ISXB4[L]=meanXstar4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISXB5=c()
for(L in 1:nn){
ISXB5[L]=meanXstar5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta46[i]=as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISXB4))-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISXB5))
}
}
}
}
IBeta45[t]=sum(IBeta46)
}
IInfBeta45=sum(IBeta45,na.rm=T)
IEndBeta45=ISusBeta412+IInfBeta45
######################################
InfBeta4=-IEndBeta45-sum(SecondBeta4)+sum(FirstBeta4)
###########################################################################################
################################################# Info Delta #####################################
#################################Cov #############################
DeltaS=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
DeltaS1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
DeltaS1[t]=SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
DeltaS[i,L]=sum(DeltaS1)
}
}
###################### infectious period ###################
DeltaI=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
DeltaI1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
DeltaI1[t]=-SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
DeltaI[i,L]=sum(DeltaI1)
}
}
DeltaIS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
DeltaIS[i,L]=DeltaS[i,L]+DeltaI[i,L]
}
}
SecondDelta=c()
for(i in 1:n){
SecondDelta[i]=mean(DeltaIS[i,]^2)
}
FirstDelta=c()
for(i in 1:n){
FirstDelta[i]=mean(DeltaIS[i,])^2
}
MDelta=c()
for(i in 1:n){
MDelta[i]=mean(DeltaIS[i,])
}
############################################################################################################
############################################################################################################
######################### Second Der...########################
IS10=rep(0,time)
for(t in 1:time){
IS9=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IS9[i]=-as.numeric(SumHnew2(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
IS10[t]=sum(IS9)
}
ISusNew10=sum(IS10)
###################### infectious period ###################
II12=rep(0,time)
for(t in 1:time){
II11=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISXD4=c()
for(L in 1:nn){
ISXD4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISXD6=c()
for(L in 1:nn){
ISXD6[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
II11[i]=as.numeric(SumHnew2(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISXD4))-as.numeric(SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISXD6))
}
}
}
}
II12[t]=sum(II11)
}
IInfeNew12=sum(II12,na.rm=T)
IEndNew12=ISusNew10+IInfeNew12
######################################
InfDelta=-IEndNew12-sum(SecondDelta)+sum(FirstDelta)
###########################################################################################
###########################################################################################
###########################################################################################
###########################################Inf alpha & beta1################################################
IAlphaBeta1=rep(0,time)
for(t in 1:time){
IAlphaBeta11=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAB1=c()
for(L in 1:nn){
IAB1[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta11[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IAB1)
}
}
}
}
IAlphaBeta1[t]=sum(IAlphaBeta11)
}
DeriveAB1=sum(IAlphaBeta1,na.rm=T)+sum(MBeta1)
AlphaBeta1=c()
for(i in 1:n){
AlphaBeta1[i]=mean(alphaIS[i,]*Beta1IS[i,])
}
InfAlBeta1=-DeriveAB1-sum(AlphaBeta1)+sum(MAlpha*MBeta1)
###########################################Inf alpha & beta2################################################
IAlphaBeta2=rep(0,time)
for(t in 1:time){
IAlphaBeta21=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAB2=c()
for(L in 1:nn){
IAB2[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta21[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IAB2)
}
}
}
}
IAlphaBeta2[t]=sum(IAlphaBeta21)
}
DeriveAB2=sum(IAlphaBeta2,na.rm=T)+sum(MBeta2)
AlphaBeta2=c()
for(i in 1:n){
AlphaBeta2[i]=mean(alphaIS[i,]*Beta2IS[i,])
}
InfAlBeta2=-DeriveAB2-sum(AlphaBeta2)+sum(MAlpha*MBeta2)
###########################################Inf alpha & beta3################################################
meanX6=function(Nlabel,Pos,Di,alpha1,beta1,beta3,beta2,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX6=0}
if(prob11!=0){
SMeanX6=Pos[L,(2*mm+i)]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanX6)
}
IAlphaBeta3=rep(0,time)
for(t in 1:time){
IAlphaBeta31=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IABx5=c()
for(L in 1:nn){
IABx5[L]=meanX6(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta31[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IABx5))
}
}
}
}
IAlphaBeta3[t]=sum(IAlphaBeta31)
}
DeriveAB3=sum(IAlphaBeta3,na.rm=T)+sum(MBeta3)
AlphaBeta3=c()
for(i in 1:n){
AlphaBeta3[i]=mean(alphaIS[i,]*Beta3IS[i,])
}
InfAlBeta3=-DeriveAB3-sum(AlphaBeta3)+sum(MAlpha*MBeta3)
###########################################Inf alpha & beta4################################################
meanXstar6=function(Nlabel,Pos,Di,alpha1,beta1,beta3,beta2,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean6=0}
if(prob11!=0){
SMean6=Pos[L,mmm]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean6)
}
IAlphaBeta4=rep(0,time)
for(t in 1:time){
IAlphaBeta41=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAB5=c()
for(L in 1:nn){
IAB5[L]=meanXstar6(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta41[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IAB5))
}
}
}
}
IAlphaBeta4[t]=sum(IAlphaBeta41)
}
DeriveAB4=sum(IAlphaBeta4,na.rm=T)+sum(MBeta4)
AlphaBeta4=c()
for(i in 1:n){
AlphaBeta4[i]=mean(alphaIS[i,]*Beta4IS[i,])
}
InfAlBeta4=-DeriveAB4-sum(AlphaBeta4)+sum(MAlpha*MBeta4)
###########################################Inf alpha & delta ################################################
IAlphaDelta1=c()
for(L in 1:nn){
IAlphaDelta2=rep(0,time)
for(t in 1:time){
IAlphaDelta3=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAlphaDelta3[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IAlphaDelta2[t]=sum(IAlphaDelta3)
}
IAlphaDelta1[L]=sum(IAlphaDelta2,na.rm=T)
}
DeriveAD=mean(IAlphaDelta1)+sum(MDelta)
AlphaDelta=c()
for(i in 1:n){
AlphaDelta[i]=mean(alphaIS[i,]*DeltaIS[i,])
}
InfAlDelta=-DeriveAD-sum(AlphaDelta)+sum(MAlpha*MDelta)
###########################################Inf beta1 & delta ################################################
Delta18=c()
for(L in 1:nn){
Delta8=rep(0,time)
for(t in 1:time){
Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Delta7[i]=cov1[i]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Delta8[t]=sum(Delta7)
}
Delta18[L]=sum(Delta8)
}
###################### infectious period ###################
Delta10=c()
for(L in 1:nn){
Delta11=rep(0,time)
for(t in 1:time){
Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Delta12[i]=-cov1[i]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Delta11[t]=sum(Delta12)
}
Delta10[L]=sum(Delta11,na.rm=T)
}
DeltaEnd=c()
for(L in 1:nn){
DeltaEnd[L]=Delta18[L]+Delta10[L]
}
Delta15=c()
for(L in 1:nn){
Delta16=rep(0,time)
for(t in 1:time){
Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Delta17[i]=cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Delta16[t]=sum(Delta17,na.rm=T)
}
Delta15[L]=sum(Delta16,na.rm=T)
}
DeriveBD=mean(Delta15)+mean(DeltaEnd)
Beta1Delta=c()
for(i in 1:n){
Beta1Delta[i]=mean(Beta1IS[i,]*DeltaIS[i,])
}
InfBeta1Delta=-DeriveBD-sum(Beta1Delta)+sum(MBeta1*MDelta)
###########################################Inf beta2 & delta ################################################
B2Delta18=c()
for(L in 1:nn){
B2Delta8=rep(0,time)
for(t in 1:time){
B2Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B2Delta7[i]=cov2[mmm]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B2Delta8[t]=sum(B2Delta7)
}
B2Delta18[L]=sum(B2Delta8)
}
###################### infectious period ###################
B2Delta10=c()
for(L in 1:nn){
B2Delta11=rep(0,time)
for(t in 1:time){
B2Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2Delta12[i]=-cov2[mmm]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2Delta11[t]=sum(B2Delta12)
}
B2Delta10[L]=sum(B2Delta11,na.rm=T)
}
B2DeltaEnd=c()
for(L in 1:nn){
B2DeltaEnd[L]=B2Delta18[L]+B2Delta10[L]
}
B2Delta15=c()
for(L in 1:nn){
B2Delta16=rep(0,time)
for(t in 1:time){
B2Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2Delta17[i]=cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2Delta16[t]=sum(B2Delta17)
}
B2Delta15[L]=sum(B2Delta16,na.rm=T)
}
DeriveB2D=mean(B2Delta15)+mean(B2DeltaEnd)
Beta2Delta=c()
for(i in 1:n){
Beta2Delta[i]=mean(Beta2IS[i,]*DeltaIS[i,])
}
InfBeta2Delta=-DeriveB2D-sum(Beta2Delta)+sum(MBeta2*MDelta)
###########################################Inf beta3& delta ################################################
B3Delta18=c()
for(L in 1:nn){
B3Delta8=rep(0,time)
for(t in 1:time){
B3Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B3Delta7[i]=SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B3Delta8[t]=sum(B3Delta7)
}
B3Delta18[L]=sum(B3Delta8)
}
###################### infectious period ###################
meanX7=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX7=0}
if(prob11!=0){
SMeanX7=Pos[L,(2*mm+i)]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanX7)
}
B3Delta10=c()
for(L in 1:nn){
B3Delta11=rep(0,time)
for(t in 1:time){
B3Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3Delta12[i]=-SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3Delta11[t]=sum(B3Delta12)
}
B3Delta10[L]=sum(B3Delta11,na.rm=T)
}
B3DeltaEnd=c()
for(L in 1:nn){
B3DeltaEnd[L]=B3Delta18[L]+B3Delta10[L]
}
B3Delta15=c()
for(L in 1:nn){
B3Delta16=rep(0,time)
for(t in 1:time){
B3Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3Delta17[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3Delta16[t]=sum(B3Delta17)
}
B3Delta15[L]=sum(B3Delta16,na.rm=T)
}
DeriveB3D=mean(B3Delta15)+mean(B3DeltaEnd)
Beta3Delta=c()
for(i in 1:n){
Beta3Delta[i]=mean(Beta3IS[i,]*DeltaIS[i,])
}
InfBeta3Delta=-DeriveB3D-sum(Beta3Delta)+sum(MBeta3*MDelta)
###########################################Inf beta4& delta ################################################
B4Delta18=c()
for(L in 1:nn){
B4Delta8=rep(0,time)
for(t in 1:time){
B4Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B4Delta7[i]=SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B4Delta8[t]=sum(B4Delta7)
}
B4Delta18[L]=sum(B4Delta8)
}
###################### infectious period ###################
meanXstar7=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXstar7=0}
if(prob11!=0){
SMeanXstar7=Pos[L,mmm]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanXstar7)
}
B4Delta10=c()
for(L in 1:nn){
B4Delta11=rep(0,time)
for(t in 1:time){
B4Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B4Delta12[i]=-SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B4Delta11[t]=sum(B4Delta12)
}
B4Delta10[L]=sum(B4Delta11,na.rm=T)
}
B4DeltaEnd=c()
for(L in 1:nn){
B4DeltaEnd[L]=B4Delta18[L]+B4Delta10[L]
}
B4Delta15=c()
for(L in 1:nn){
B4Delta16=rep(0,time)
for(t in 1:time){
B4Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B4Delta17[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B4Delta16[t]=sum(B4Delta17)
}
B4Delta15[L]=sum(B4Delta16,na.rm=T)
}
DeriveB4D=mean(B4Delta15)+mean(B4DeltaEnd)
Beta4Delta=c()
for(i in 1:n){
Beta4Delta[i]=mean(Beta4IS[i,]*DeltaIS[i,])
}
InfBeta4Delta=-DeriveB4D-sum(Beta4Delta)+sum(MBeta4*MDelta)
########################################### beta1 & beta 2 ################################################################
B1Beta21=c()
for(L in 1:nn){
B1NewBeta21=rep(0,time)
for(t in 1:time){
B1NewBeta22=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B1NewBeta22[i]=-cov1[i]*cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B1NewBeta21[t]=sum(B1NewBeta22)
}
B1Beta21[L]=sum(B1NewBeta21)
}
###################### infectious period ###################
B1InfBeta23=c()
for(L in 1:nn){
B1NewBeta23=rep(0,time)
for(t in 1:time){
B1NewBeta24=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B1NewBeta24[i]=cov1[i]*cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B1NewBeta23[t]=sum(B1NewBeta24)
}
B1InfBeta23[L]=sum(B1NewBeta23,na.rm=T)
}
New23Beta=c()
for(L in 1:nn){
New23Beta[L]=B1Beta21[L]+B1InfBeta23[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta1Beat2=c()
for(L in 1:nn){
IBeta25=rep(0,time)
for(t in 1:time){
IBeta26=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IBeta26[i]=-cov1[i]*cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IBeta25[t]=sum(IBeta26)
}
Beta1Beat2[L]=sum(IBeta25,na.rm=T)
}
DeriveBeta1Beat2=mean(Beta1Beat2)+mean(New23Beta)
Beta1Beat21=c()
for(i in 1:n){
Beta1Beat21[i]=mean(Beta1IS[i,]*Beta2IS[i,])
}
InfBeta1Beat2=-DeriveBeta1Beat2-sum(Beta1Beat21)+sum(MBeta1*MBeta2)
########################################### beta1 & beta 3 ################################################################
B1Bet1a31=c()
for(L in 1:nn){
B1NewBeta31=rep(0,time)
for(t in 1:time){
B1NewBeta32=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B1NewBeta32[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B1NewBeta31[t]=sum(B1NewBeta32)
}
B1Bet1a31[L]=sum(B1NewBeta31)
}
###################### infectious period ###################
B1NewInfBeta33=c()
for(L in 1:nn){
B1NewBeta33=rep(0,time)
for(t in 1:time){
B1NewBeta34=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B1NewBeta34[i]=cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B1NewBeta33[t]=sum(B1NewBeta34)
}
B1NewInfBeta33[L]=sum(B1NewBeta33,na.rm=T)
}
B1EndBeta33=c()
for(L in 1:nn){
B1EndBeta33[L]=B1Bet1a31[L]+B1NewInfBeta33[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta1Beta3=c()
for(L in 1:nn){
IBeta35=rep(0,time)
for(t in 1:time){
IBeta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IBeta36[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IBeta35[t]=sum(IBeta36)
}
Beta1Beta3[L]=sum(IBeta35,na.rm=T)
}
DeriveBeta1Beta3=mean(Beta1Beta3)+mean(B1EndBeta33)
Beta1Beat31=c()
for(i in 1:n){
Beta1Beat31[i]=mean(Beta1IS[i,]*Beta3IS[i,])
}
InfBeta3Beta1=-DeriveBeta1Beta3-sum(Beta1Beat31)+sum(MBeta1*MBeta3)
########################################### beta1 & beta 4 ################################################################
B1Bet1a41=c()
for(L in 1:nn){
B1NewBeta41=rep(0,time)
for(t in 1:time){
B1NewBeta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B1NewBeta42[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B1NewBeta41[t]=sum(B1NewBeta42)
}
B1Bet1a41[L]=sum(B1NewBeta41)
}
###################### infectious period ###################
B1NewInfBeta43=c()
for(L in 1:nn){
B1NewBeta43=rep(0,time)
for(t in 1:time){
B1NewBeta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B1NewBeta44[i]=cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B1NewBeta43[t]=sum(B1NewBeta44)
}
B1NewInfBeta43[L]=sum(B1NewBeta43,na.rm=T)
}
B1EndBeta43=c()
for(L in 1:nn){
B1EndBeta43[L]=B1Bet1a41[L]+B1NewInfBeta43[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta1Beta4=c()
for(L in 1:nn){
IBeta45=rep(0,time)
for(t in 1:time){
IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IBeta46[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanXstar7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IBeta45[t]=sum(IBeta46)
}
Beta1Beta4[L]=sum(IBeta45,na.rm=T)
}
DeriveBeta1Beta4=mean(Beta1Beta4)+mean(B1EndBeta43)
Beta1Beat41=c()
for(i in 1:n){
Beta1Beat41[i]=mean(Beta1IS[i,]*Beta4IS[i,])
}
InfBeta4Beta1=-DeriveBeta1Beta4-sum(Beta1Beat41)+sum(MBeta1*MBeta4)
########################################### beta2 & beta 3 ################################################################
B2Beta31=c()
for(L in 1:nn){
B2NewBeta31=rep(0,time)
for(t in 1:time){
B2NewBeta32=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B2NewBeta32[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B2NewBeta31[t]=sum(B2NewBeta32)
}
B2Beta31[L]=sum(B2NewBeta31)
}
###################### infectious period ###################
B2NewInfBeta33=c()
for(L in 1:nn){
B2NewBeta33=rep(0,time)
for(t in 1:time){
B2NewBeta34=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2NewBeta34[i]=cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2NewBeta33[t]=sum(B2NewBeta34)
}
B2NewInfBeta33[L]=sum(B2NewBeta33,na.rm=T)
}
B2EndBeta33=c()
for(L in 1:nn){
B2EndBeta33[L]=B2Beta31[L]+B2NewInfBeta33[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta2Beta3=c()
for(L in 1:nn){
B2IBeta35=rep(0,time)
for(t in 1:time){
B2IBeta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2IBeta36[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2IBeta35[t]=sum(B2IBeta36)
}
Beta2Beta3[L]=sum(B2IBeta35,na.rm=T)
}
DeriveBeta2Beta3=mean(Beta2Beta3)+mean(B2EndBeta33)
Beta2Beat31=c()
for(i in 1:n){
Beta2Beat31[i]=mean(Beta2IS[i,]*Beta3IS[i,])
}
InfBeta3Beta2=-DeriveBeta2Beta3-sum(Beta2Beat31)+sum(MBeta2*MBeta3)
########################################### beta2 & beta 4 ################################################################
B2Beta41=c()
for(L in 1:nn){
B2NewBeta41=rep(0,time)
for(t in 1:time){
B2NewBeta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B2NewBeta42[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B2NewBeta41[t]=sum(B2NewBeta42)
}
B2Beta41[L]=sum(B2NewBeta41)
}
###################### infectious period ###################
B2NewInfBeta43=c()
for(L in 1:nn){
B2NewBeta43=rep(0,time)
for(t in 1:time){
B2NewBeta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2NewBeta44[i]=cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2NewBeta43[t]=sum(B2NewBeta44)
}
B2NewInfBeta43[L]=sum(B2NewBeta43,na.rm=T)
}
B2EndBeta43=c()
for(L in 1:nn){
B2EndBeta43[L]=B2Beta41[L]+B2NewInfBeta43[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta2Beta4=c()
for(L in 1:nn){
B2IBeta45=rep(0,time)
for(t in 1:time){
B2IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2IBeta46[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanXstar7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2IBeta45[t]=sum(B2IBeta46)
}
Beta2Beta4[L]=sum(B2IBeta45,na.rm=T)
}
DeriveBeta2Beta4=mean(Beta2Beta4)+mean(B2EndBeta43)
Beta2Beat41=c()
for(i in 1:n){
Beta2Beat41[i]=mean(Beta2IS[i,]*Beta4IS[i,])
}
InfBeta4Beta2=-DeriveBeta2Beta4-sum(Beta2Beat41)+sum(MBeta2*MBeta4)
#######################################################################################################
########################################### beta3 & beta 4 ################################################################
B3Beta41=c()
for(L in 1:nn){
B3NewBeta41=rep(0,time)
for(t in 1:time){
B3NewBeta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B3NewBeta42[i]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B3NewBeta41[t]=sum(B3NewBeta42)
}
B3Beta41[L]=sum(B3NewBeta41)
}
###################### infectious period ###################
meanXX2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXX2=0}
if(prob11!=0){
SMeanXX2=Pos[L,(2*mm+i)]*Pos[L,mmm]*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanXX2)
}
meanXX7=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXX7=0}
if(prob11!=0){
SMeanXX7=Pos[L,(2*mm+i)]*Pos[L,mmm]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanXX7)
}
B3NewInfBeta43=c()
for(L in 1:nn){
B3NewBeta43=rep(0,time)
for(t in 1:time){
B3NewBeta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3NewBeta44[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3NewBeta43[t]=sum(B3NewBeta44)
}
B3NewInfBeta43[L]=sum(B3NewBeta43,na.rm=T)
}
B3EndBeta43=c()
for(L in 1:nn){
B3EndBeta43[L]=B3Beta41[L]+B3NewInfBeta43[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta3Beta4=c()
for(L in 1:nn){
B3IBeta45=rep(0,time)
for(t in 1:time){
B3IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3IBeta46[i]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanXX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3IBeta45[t]=sum(B3IBeta46)
}
Beta3Beta4[L]=sum(B3IBeta45,na.rm=T)
}
DeriveBeta3Beta4=mean(Beta3Beta4)+mean(B3EndBeta43)
Beta3Beat41=c()
for(i in 1:n){
Beta3Beat41[i]=mean(Beta3IS[i,]*Beta4IS[i,])
}
InfBeta3Beta4=-DeriveBeta3Beta4-sum(Beta3Beat41)+sum(MBeta3*MBeta4)
A1=c(InfAlpha,InfAlBeta1,InfAlBeta2,InfAlBeta3,InfAlBeta4,InfAlDelta)
A2=c(InfAlBeta1,InfBeta1,InfBeta1Beat2,InfBeta3Beta1,InfBeta4Beta1,InfBeta1Delta)
A3=c(InfAlBeta2,InfBeta1Beat2,InfBeta2,InfBeta3Beta2,InfBeta4Beta2,InfBeta2Delta)
A4=c(InfAlBeta3,InfBeta3Beta1,InfBeta3Beta2,InfBeta3,InfBeta3Beta4,InfBeta3Delta)
A5=c(InfAlBeta4,InfBeta4Beta1,InfBeta4Beta2,InfBeta3Beta4,InfBeta4,InfBeta4Delta)
A6=c(InfAlDelta,InfBeta1Delta,InfBeta2Delta,InfBeta3Delta,InfBeta4Delta,InfDelta)
ObservedInf=rbind(A1,A2,A3,A4,A5,A6)
Variances=diag(solve(ObservedInf))
Variances
CInfAlpha=-IEndA5
CInfBeta1=-IEndBeta15
CInfBeta2=-IEndBeta25
CInfBeta3=-IEndBeta35
CInfBeta4=-IEndBeta45
CInfDelta=-IEndNew12
CInfAlBeta1=-DeriveAB1
CInfAlBeta2=-DeriveAB2
CInfAlBeta3=-DeriveAB3
CInfAlBeta4=-DeriveAB4
CInfAlDelta=-DeriveAD
CInfBeta1Delta=-DeriveBD
CInfBeta2Delta=-DeriveB2D
CInfBeta3Delta=-DeriveB3D
CInfBeta4Delta=-DeriveB4D
CInfBeta1Beat2=-DeriveBeta1Beat2
CInfBeta3Beta1=-DeriveBeta1Beta3
CInfBeta4Beta1=-DeriveBeta1Beta4
CInfBeta3Beta2=-DeriveBeta2Beta3
CInfBeta4Beta2=-DeriveBeta2Beta4
CInfBeta3Beta4=-DeriveBeta3Beta4
CA1=c(CInfAlpha,CInfAlBeta1,CInfAlBeta2,CInfAlBeta3,CInfAlBeta4,CInfAlDelta)
CA2=c(CInfAlBeta1,CInfBeta1,CInfBeta1Beat2,CInfBeta3Beta1,CInfBeta4Beta1,CInfBeta1Delta)
CA3=c(CInfAlBeta2,CInfBeta1Beat2,CInfBeta2,CInfBeta3Beta2,CInfBeta4Beta2,CInfBeta2Delta)
CA4=c(CInfAlBeta3,CInfBeta3Beta1,CInfBeta3Beta2,CInfBeta3,CInfBeta3Beta4,CInfBeta3Delta)
CA5=c(CInfAlBeta4,CInfBeta4Beta1,CInfBeta4Beta2,CInfBeta3Beta4,CInfBeta4,CInfBeta4Delta)
CA6=c(CInfAlDelta,CInfBeta1Delta,CInfBeta2Delta,CInfBeta3Delta,CInfBeta4Delta,CInfDelta)
CObservedInf=rbind(CA1,CA2,CA3,CA4,CA5,CA6)
CVariances=diag(solve(CObservedInf))
CVariances
######################################Spatial parameters##########################################
QLoglik11=function(par){
sigma1=par[[1]]
lambda1=par[[2]]
Log1=c()
for(L in 1:nn){
Log1[L]=dmvnorm(Pos[L,(mm+1):(2*mm)], rep(0,mm), sigma1^2*solve((lambda1*D+(1-lambda1)*I)), log = T)
}
LLL=mean(Log1)
return(LLL)
}
Hes=hessian(QLoglik11,c(sigma1,lambda1))
VarSpatial=diag(solve(-Hes))
result=list(CVariances=CVariances,VarSpatial=VarSpatial,ObservedInf=ObservedInf,Variances=Variances)
result
}
#######################Data Generation and Results################
######################################################
#start of loop for simulation
CovMEA=matrix(0,ITER,mm)
CovMEInd=matrix(0,ITER,n)
GePHI=matrix(0,ITER,mm)
for(iter in 1:ITER){
I=diag(mm)
mu=rep(0,mm)
Sigma0=sigma0^2*solve((lambda0*D+(1-lambda0)*I))
det(Sigma0)
GePHI[iter,]=mvrnorm(1, mu, Sigma0, tol = 1e-6)
############################################################
###########################
x=data[,1,iter]
y=data[,2,iter]
########################
Di=matrix(0,n,n)
for(i in 1:n){
for(j in 1:n){
Di[i,j]=sqrt((x[i]-x[j])^2+(y[i]-y[j])^2)
}
}
Di=Di*100
##########
vv=CovXStar1
ww=CovX
phi=GePHI[iter,]
for(t in 1:time){
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]== 0){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta0)
}
}
}
dx=sum(dx1)
P=1-exp(-exp(alpha0+beta10*cov1[i]+beta20*cov2[mmm]+beta30*CovX[i]+beta40*CovXStar1[mmm]+phi[mmm])*dx)
u=runif(1,0,1)
if(P>u){
tau[i]=t+1
}
}
}
}
}
}
tau
####################################################################################
####################################################################################
LA=c()
ss=1
est0=estfunNaiv(Nlabel,phi,Di,alpha0,beta10,beta20,beta30,beta40,delta0,sigma0,lambda0,D,lambda)
alpha1=est0$alpha1
delta=est0$delta
lambda1=est0$lambda1
sigma1=est0$sigma1
beta1=est0$beta1
beta2=est0$beta2
beta3=est0$beta3
beta4=est0$beta4
Pos1=est0$Pos1
if(is.na(alpha1)|is.na(delta)|is.na(lambda1)|is.na(sigma1)|is.na(beta1)|is.na(beta2)|is.na(beta3)|is.na(beta4)){
LA[1]=NA
}
if(!is.na(alpha1)&&!is.na(delta)&&!is.na(lambda1)&&!is.na(sigma1)&&!is.na(beta1)&&!is.na(beta2)&&!is.na(beta3)&&!is.na(beta4)){
LA[1]=LogNaiv(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda)
}
repeat{
ss=ss+1
if(is.na(LA[1])){
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=NA)
break
}
if(ss>25){
alpha1=NA
delta=NA
sigma1=NA
lambda1=NA
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=NA)
break
}
if(!is.na(alpha1)&&!is.na(delta)&&!is.na(lambda1)&&!is.na(sigma1)&&!is.na(beta1)&&!is.na(beta2)&&!is.na(beta3)&&!is.na(beta4)){
if(sigma1<0 |lambda1>1|lambda1<0|delta<0){
alpha1=NA
delta=NA
sigma1=NA
lambda1=NA
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=ss)
break
}
}
E0=c(alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1)
LA
est=estfunNaiv(Nlabel,phi,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda)
alpha1=est$alpha1
delta=est$delta
lambda1=est$lambda1
sigma1=est$sigma1
beta1=est$beta1
beta2=est$beta2
beta3=est$beta3
beta4=est$beta4
Pos1=est$Pos1
if(!is.na(alpha1)&&!is.na(delta)&&!is.na(lambda1)&&!is.na(sigma1)&&!is.na(beta1)&&!is.na(beta2)&&!is.na(beta3)&&!is.na(beta4)){
if(sigma1<0 |lambda1>1|lambda1<0|delta<0){
alpha1=NA
delta=NA
sigma1=NA
lambda1=NA
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=ss)
break
}
if(sigma1>=0 & lambda1<=1 & lambda1>=0){
E1=c(alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1)
Dist=sqrt(sum((E0-E1)^2))
LA[ss]=LogNaiv(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda)
out1=list(LA=LA,Pos1=Pos1,alpha1=alpha1,beta1=beta1,beta2=beta2,beta3=beta3,beta4=beta4,delta=delta,sigma1=sigma1,lambda1=lambda1,ss=ss,E1=E1,E0=E0)
if(!abs((LA[ss]-LA[ss-1])/LA[ss])>eps){
break
}
}
}
if(is.na(alpha1)|is.na(delta)|is.na(lambda1)|is.na(sigma1)|is.na(beta1)|is.na(beta2)|is.na(beta3)|is.na(beta4)){
out1=list(alpha1=NA,beta1=NA,beta2=NA,beta3=NA,beta4=NA,delta=NA,sigma1=NA,lambda1=NA)
break
}
}
NaivPos=Pos1
NaivEstpar=c(alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1)
NaivFinalInf=ObsInfNaiv(Nlabel,NaivPos,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,lambda)
if(is.na(sigma1)){
NaivSimPAR[iter,]=NA
NaivSimVarPar[iter,]=NA
NaivCSimVarPar[iter,]=NA
NaivSimInfPar[iter,]=NA
NaivSimVarSpatial[iter,]=NA
NaivSimPos[[iter]]=NA
}
if(!is.na(sigma1)){
NaivSimPAR[iter,]=NaivEstpar
NaivSimVarPar[iter,]=NaivFinalInf$Variances
NaivSimInfPar[iter,]=diag(NaivFinalInf$ObservedInf)
NaivSimVarSpatial[iter,]=(NaivFinalInf$VarSpatial)
NaivSimPos[[iter]]=NaivPos
NaivCSimVarPar[iter,]=NaivFinalInf$CVariances
}
}
result=list(NaivSimPAR=NaivSimPAR,NaivSimVarPar=NaivSimVarPar,NaivSimVarSpatial=NaivSimVarSpatial,NaivSimPos=NaivSimPos,NaivCSimVarPar=NaivCSimVarPar)
}
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Defines functions NaiveEstimation
Documented in NaiveEstimation
#' Estimating parameters along with corresponding variances based on Naive model.
#'
#' @param ITER The number of simulation runs
#' @param MHiteration The number of iterations in Metropolis–Hastings algorithm
#' @param eps Stopping value for MCECM algorithm
#' @param d distance between cells
#' @param nSample number of sample in each cell
#' @param mm Number of areas.
#' @param time Maximum time.
#' @param MuxStar0 Mean of unobserved areal level covariates.
#' @param MuxInd0 Mean of unobserved individual level covariates.
#' @param SigmaxStar0 Variance of unobserved areal level covariates.
#' @param SigmaxInd0 Variance of unobserved individual level covariates.
#' @param Sigmav0 Variance of areal level measurement error variable.
#' @param Sigmaw0 Variance of individual level measurement error variable.
#' @param lambda0 Spatial dependency parameter.
#' @param sigma0 Over dispersion parameter.
#' @param delta0 The spatial parameter.
#' @param alpha0 Initial value for intercept.
#' @param beta10 Initial value for coefficient of observed individual level covariates.
#' @param beta20 Initial value for coefficient of observed areal level covariates.
#' @param beta30 Initial value for coefficient of unobserved individual level covariates.
#' @param beta40 Initial value for coefficient of unobserved areal level covariates.
#' @param InfPeriod The infectious period length.
#' @param g grid dimension
#'
#' @return The results of the function
#'
#' @export
#'
#' @importFrom mvtnorm dmvnorm
#' @importFrom MASS mvrnorm
#' @importFrom numDeriv hessian
#' @importFrom stats optim
#' @importFrom stats rnorm
#' @importFrom stats dnorm
#' @importFrom stats runif
#' @importFrom ngspatial adjacency.matrix
#' @importFrom corpcor make.positive.definite
#' @importFrom psych tr
#'
#'
#' @examples NaiveEstimation(1,5,0.05,2,4,4,20,0,0,1,1,0.3,0.3,0.5,0.5,2.5,0,1,
#' 1,1,1,3,2)
#'
#'
NaiveEstimation=function(ITER,MHiteration,eps,d,nSample,mm,time,MuxStar0,MuxInd0,SigmaxStar0,SigmaxInd0,Sigmav0,Sigmaw0,lambda0,sigma0,delta0,alpha0,beta10,beta20,beta30,beta40,InfPeriod,g){
############################a######Generate Data############################
nn=MHiteration
N = rep(nSample,(g^2))
n=sum(N)
i=n
NaivSimPAR=matrix(0,ITER,8)
NaivSimVarPar=matrix(0,ITER,6)
NaivCSimVarPar=matrix(0,ITER,6)
NaivSimInfPar=matrix(0,ITER,6)
NaivSimVarSpatial=matrix(0,ITER,2)
NaivSimPos=list()
lambda=rep(InfPeriod,n) #########ifected period##############
I=diag(mm)
A1=adjacency.matrix(g, g)
A2=colSums(A1)
D=-A1
diag(D)=A2
###############################Covaraites without measurement error#######################
cov1=rnorm(n,0,1)
cov2=rnorm(mm,0,1)
#####################infected time #####################
D1=c()
for(mmm in 1:mm){
D1[mmm]=sample(N[mmm],1,replace=F)
}
D1
tau1=list()
for(i in 1:mm){
tau1[[i]]=rep(0,N[i])
tau1[[i]][D1[i]]=1
}
tau=unlist(tau1)
Nlabel1=list()
for(i in 1:mm){
Nlabel1[[i]]=rep(i,N[i])
}
Nlabel=unlist(Nlabel1)
Newlabel=matrix(0,n,mm)
for(mmm in 1:mm){
Newlabel[,mmm]=rep(D[,mmm],N)
}
CovXStar1=rnorm(mm, MuxStar0, sqrt(SigmaxStar0))
CovX=rnorm(n, MuxInd0, sqrt(SigmaxInd0))
data=array(0,c(n,2,ITER))
for (iter in 1:ITER) {
xx = c(rep(0,nSample*g*g))
for (gg in 1:g) {
x=matrix(0,nSample,g)
for(i in 1:g){
x[,i]=runif(nSample,d*(gg-1),d*gg)
}
v=nSample*gg*g
xx[1:v] = c(x)
}
X=c(xx)
yy = c(rep(0,nSample*g*g))
for (gg in 1:g) {
y=matrix(0,nSample,gg)
for(i in 1:gg){
y[,i]=runif(nSample,d*(i-1),d*i)
}
z=nSample*gg*g
yy[1:z] = c(y)
}
Y = c(yy)
data[,,iter]=cbind(X,Y)
}
############################## f_y|x,xStar,u###############################
Fy1=function(IndLe,AreLe,RaE,alpha1,beta1,beta2,beta3,beta4,delta,time,tau,mm,lambda){
fy1=array(0,c(n,time,mm))
for(i in 1:n){
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob1=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*IndLe[i]+beta4*AreLe[mmm]+RaE[mmm])*dx)
fy1[i,t,mmm]=(1-prob1)
}
if (tau[i]==(t+1)){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob1=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*IndLe[i]+beta4*AreLe[mmm]+RaE[mmm])*dx)
fy1[i,t,mmm]=prob1
}
}
}
}
}
PP=c()
H=list()
fy2=c()
for(mmm in 1:mm){
for(i in 1:n){
PP[i]=round(prod(fy1[i,,mmm][fy1[i,,mmm]>0]),10)
}
H[[mmm]]=which(PP!=1)
fy2[mmm]=prod(PP[H[[mmm]]][PP[H[[mmm]]]>0])
}
return(fy2)
}
##############################################################################################
fRanE=function(RaE,mmm,lambda1,sigma1,D){
Nh=-D[,mmm]*RaE
dnorm(RaE[mmm],lambda1/(1-lambda1+D[mmm,mmm]*lambda1)*sum(Nh[-mmm]),sqrt(1/(sigma1^2*(1-lambda1+D[mmm,mmm]*lambda1))), log = FALSE)
}
#################Sum h(z-z_{I}) #######################
SumH=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH1[j]=Di[i,j]^(-delta)
}
}
}
SumH1=replace(SumH1,is.infinite(SumH1),0)
SumH2=sum(SumH1)
SumH3=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH2
return(SumH3)
}
#################Sum h(z-z_{I})log(d_{ij}) #######################
SumHnew1=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH4=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH4[j]=Di[i,j]^(-delta)*(log(Di[i,j]))
}
}
}
SumH4=replace(SumH4,is.infinite(SumH4),0)
SumH5=sum(SumH4)
SumH6=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH5
return(SumH6)
}
#################Sum h(z-z_{I})(log(d_{ij}))^2 #######################
SumHnew2=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH7=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH7[j]=Di[i,j]^(-delta)*(log(Di[i,j]))^2
}
}
}
SumH7=replace(SumH7,is.infinite(SumH7),0)
SumH8=sum(SumH7)
SumH9=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH8
return(SumH9)
}
E.sigma.first=function(Pos,D,lambda1){
d1=c()
for(L in 1:nn){
d1[L]=as.numeric(t(Pos[L,(mm+1):(2*mm)])%*%(lambda1*D+(1-lambda1)*I)%*%Pos[L,(mm+1):(2*mm)])
}
SMeansigma1=mean(d1)
return(SMeansigma1)
}
E.lambda1.first=function(Pos,D){
d2=c()
for(L in 1:nn){
d2[L]= as.numeric(t(Pos[L,(mm+1):(2*mm)])%*%(D-I)%*%Pos[L,(mm+1):(2*mm)])
}
SMeanlambda11=mean(d2)
return(SMeanlambda11)
}
######################################### Expectation #######################
mean1=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMean1=mean(d1)
return(SMean1)
}
meanXstar1=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanXstar1=mean(d1)
return(SMeanXstar1)
}
meanX1=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanX1=mean(d1)
return(SMeanX1)
}
meanXstar3=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,mmm]^2*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanXstar3=mean(d1)
return(SMeanXstar3)
}
meanX3=function(Pos,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=Pos[L,(2*mm+i)]^2*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
SMeanX3=mean(d1)
return(SMeanX3)
}
###############################################################
mean2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,(mmm+mm)])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean2=0}
if(prob11!=0){
SMean2=(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMean2)
}
meanXstar2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXstar2=0}
if(prob11!=0){
SMeanXstar2=Pos[L,mmm]*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanXstar2)
}
meanX2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX2=0}
if(prob11!=0){
SMeanX2=Pos[L,(2*mm+i)]*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanX2)
}
meanXstar4=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXstar4=0}
if(prob11!=0){
SMeanXstar4=Pos[L,mmm]^2*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanXstar4)
}
meanX4=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX4=0}
if(prob11!=0){
SMeanX4=Pos[L,(2*mm+i)]^2*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanX4)
}
####################################################################
mean3=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean3=0}
if(prob11!=0){
SMean3=(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]++2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean3)
}
meanXstar5=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean5=0}
if(prob11!=0){
SMean5=Pos[L,mmm]^2*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean5)
}
meanX5=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean5=0}
if(prob11!=0){
SMean5=Pos[L,(2*mm+i)]^2*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean5)
}
############################################################################################################################
estfunNaiv=function(Nlabel,phi,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda){
##################M-H###############################
nn=MHiteration
AreLe0=vv
IndLe0=ww
mu=rep(0,mm)
Sigma11=sigma1^2*solve((lambda1*D+(1-lambda1)*I))
Sigma1 = make.positive.definite(Sigma11, tol = 1e-3)
RaE0=mvrnorm(1, mu, Sigma11, tol = 1e-6)
First=c(AreLe0,RaE0,IndLe0)
Pos=matrix(0,nrow=nn+1,ncol=((2*mm)+n))
Pos[1,]=First
MPHprob3=matrix(0,nn,n)
Uni3=matrix(0,nn,n)
MPHprob1=matrix(0,nn,mm)
Uni1=matrix(0,nn,mm)
MPHprob2=c()
Uni2=c()
for (L in 2:nn){
AreLe=vv
IndLe=ww
RaE=mvrnorm(1, mu, Sigma11, tol = 1e-6)
Pos[L,(2*mm+1):(2*mm+n)]=IndLe
Pos[L,1:mm]=AreLe
Area_sec3=Fy1(Pos[L-1,(2*mm+1):(2*mm+n)],Pos[L-1,1:mm],RaE,alpha1,beta1,beta2,beta3,beta4,delta,time,tau,mm,lambda)
Area_sec4=Fy1(Pos[L-1,(2*mm+1):(2*mm+n)],Pos[L-1,1:mm],Pos[L-1,(mm+1):(2*mm)],alpha1,beta1,beta2,beta3,beta4,delta,time,tau,mm,lambda)
Uni2[L]=runif(1,0,1)
MPHprob2[L]=min(1,prod(Area_sec3/Area_sec4))
if(Uni2[L]<MPHprob2[L]){
Pos[L,(mm+1):(2*mm)]=RaE
}
if(Uni2[L]>=MPHprob2[L]){
Pos[L,(mm+1):(2*mm)]=Pos[L-1,(mm+1):(2*mm)]
}
}
######################################## alpha #######################################
NewtonAlpha=function(Newalpha1){
A1=rep(0,time)
for(t in 1:time){
A2=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
A2[i]=-as.numeric(SumH(Nlabel,Di,Newalpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
A1[t]=sum(A2)
}
SusA1=sum(A1)
###################### infectious period ###################
A3=rep(0,time)
for(t in 1:time){
A4=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SA4=c()
for(L in 1:nn){
SA4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
A4[i]=mean(SA4)*SumH(Nlabel,Di,Newalpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
A3[t]=sum(A4)
}
InfA3=sum(A3,na.rm=T)
EndA3=SusA1+InfA3
######################### Second Der...########################
##################### infectious period ###################
A5=rep(0,time)
for(t in 1:time){
A6=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SA6=c()
for(L in 1:nn){
SA6[L]=-mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
A6[i]=mean(SA6)*SumH(Nlabel,Di,Newalpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2
}
}
}
}
A5[t]=sum(A6)
}
InfA5=sum(A5,na.rm=T)
EndA5=EndA3+InfA5
EstAlpha1=Newalpha1-EndA3/EndA5
diffAlpha=EstAlpha1-Newalpha1
result=list(Newalpha1=EstAlpha1,diffAlpha=diffAlpha)
result
}
talpha=1
Nalpha0=NewtonAlpha(alpha1)
diffAlpha=Nalpha0$diffAlpha
Newalpha1=Nalpha0$Newalpha1
EstAlpha=Newalpha1
#################################beta1##################################
NewtonBeat1=function(Newbeta1){
Beta11=rep(0,time)
for(t in 1:time){
Beta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta12[i]=-cov1[i]*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta11[t]=sum(Beta12)
}
SusBeta11=sum(Beta11)
###################### infectious period ###################
Beta13=rep(0,time)
for(t in 1:time){
Beta14=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB4=c()
for(L in 1:nn){
SB4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta14[i]=cov1[i]*mean(SB4)*SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
Beta13[t]=sum(Beta14)
}
InfBeta13=sum(Beta13,na.rm=T)
EndBeta13=SusBeta11+InfBeta13
######################### Second Der...########################
##################### infectious period ###################
Beta112=rep(0,time)
for(t in 1:time){
Beta122=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta122[i]=-cov1[i]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta112[t]=sum(Beta122)
}
SusBeta112=sum(Beta112)
Beta15=rep(0,time)
for(t in 1:time){
Beta16=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB6=c()
for(L in 1:nn){
SB6[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SB8=c()
for(L in 1:nn){
SB8[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta16[i]=cov1[i]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)*mean(SB6))-cov1[i]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,Newbeta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(SB8))
}
}
}
}
Beta15[t]=sum(Beta16)
}
InfBeta15=sum(Beta15,na.rm=T)
EndBeta15=SusBeta112+InfBeta15
EstBeta1New1=Newbeta1-EndBeta13/EndBeta15
diffBeat1=EstBeta1New1-Newbeta1
result=list(Newbeta1=EstBeta1New1,diffBeat1=diffBeat1)
result
}
if(is.na(EstAlpha)){
EstBeta1=NA
}
if(!is.na(EstAlpha)){
tbeta1=1
Nbeta10=NewtonBeat1(beta1)
diffBeat1=Nbeta10$diffBeat1
Newbeta1=Nbeta10$Newbeta1
EstBeta1=Newbeta1
}
#################################beta2##################################
NewtonBeat2=function(Newbeta2){
Beta21=rep(0,time)
for(t in 1:time){
Beta22=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta22[i]=-cov2[mmm]*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta21[t]=sum(Beta22)
}
SusBeta21=sum(Beta21)
###################### infectious period ###################
Beta23=rep(0,time)
for(t in 1:time){
Beta24=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB10=c()
for(L in 1:nn){
SB10[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta24[i]=cov2[mmm]*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean(SB10))
}
}
}
}
Beta23[t]=sum(Beta24)
}
InfBeta23=sum(Beta23,na.rm=T)
EndBeta23=SusBeta21+InfBeta23
######################### Second Der...########################
##################### infectious period ###################
Beta212=rep(0,time)
for(t in 1:time){
Beta222=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta222[i]=-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta212[t]=sum(Beta222)
}
SusBeta212=sum(Beta212)
Beta25=rep(0,time)
for(t in 1:time){
Beta26=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SB12=c()
for(L in 1:nn){
SB12[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SB14=c()
for(L in 1:nn){
SB14[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta26[i]=cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)*mean(SB12))-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,Newbeta2,delta,i,mmm,t,tau,lambda)^2*mean(SB14))
}
}
}
}
Beta25[t]=sum(Beta26)
}
InfBeta25=sum(Beta25,na.rm=T)
EndBeta25=SusBeta212+InfBeta25
##################################################################
EstBeta2New1=Newbeta2-EndBeta23/EndBeta25
diffBeat2=EstBeta2New1-Newbeta2
result=list(Newbeta2=EstBeta2New1,diffBeat2=diffBeat2)
result
}
if(is.na(EstBeta1)){
EstBeta2=NA
}
if(!is.na(EstBeta1)){
tbeta2=1
Nbeta20=NewtonBeat2(beta2)
diffBeat2=Nbeta20$diffBeat2
Newbeta2=Nbeta20$Newbeta2
EstBeta2=Newbeta2
}
if(is.na(EstBeta2)){
EstBeta3=NA
}
if(!is.na(EstBeta2)){
#################################beta4##################################
Beta31=rep(0,time)
for(t in 1:time){
Beta32=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta32[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanX1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta31[t]=sum(Beta32)
}
SusBeta31=sum(Beta31)
###################### infectious period ###################
Beta33=rep(0,time)
for(t in 1:time){
Beta34=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB13=c()
for(L in 1:nn){
SXB13[L]=meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta34[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB13))
}
}
}
}
Beta33[t]=sum(Beta34)
}
InfBeta33=sum(Beta33,na.rm=T)
EndBeta33=SusBeta31+InfBeta33
######################### Second Der...########################
##################### infectious period ###################
Beta312=rep(0,time)
for(t in 1:time){
Beta322=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta322[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanX3(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta312[t]=sum(Beta322)
}
SusBeta312=sum(Beta312)
Beta35=rep(0,time)
for(t in 1:time){
Beta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB23=c()
for(L in 1:nn){
SXB23[L]=meanX4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SXB53=c()
for(L in 1:nn){
SXB53[L]=meanX5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta36[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB23))-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)^2*mean(SXB53))
}
}
}
}
Beta35[t]=sum(Beta36)
}
InfBeta35=sum(Beta35,na.rm=T)
EndBeta35=SusBeta312+InfBeta35
EstBeta3=beta3-EndBeta33/EndBeta35
EstBeta3
}
##################################################################
if(is.na(EstBeta3)){
EstBeta4=NA
}
if(!is.na(EstBeta3)){
#################################beta4##################################
Beta41=rep(0,time)
for(t in 1:time){
Beta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta42[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanXstar1(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta41[t]=sum(Beta42)
}
SusBeta41=sum(Beta41)
###################### infectious period ###################
Beta43=rep(0,time)
for(t in 1:time){
Beta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB2=c()
for(L in 1:nn){
SXB2[L]=meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta44[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB2))
}
}
}
}
Beta43[t]=sum(Beta44)
}
InfBeta43=sum(Beta43,na.rm=T)
EndBeta43=SusBeta41+InfBeta43
######################### Second Der...########################
##################### infectious period ###################
Beta412=rep(0,time)
for(t in 1:time){
Beta422=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta422[i]=-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*meanXstar3(Pos,beta3,beta4,mmm,i))
}
}
}
}
Beta412[t]=sum(Beta422)
}
SusBeta412=sum(Beta412)
Beta45=rep(0,time)
for(t in 1:time){
Beta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXB4=c()
for(L in 1:nn){
SXB4[L]=meanXstar4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SXB5=c()
for(L in 1:nn){
SXB5[L]=meanXstar5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
Beta46[i]=as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)*mean(SXB4))-as.numeric(SumH(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,delta,i,mmm,t,tau,lambda)^2*mean(SXB5))
}
}
}
}
Beta45[t]=sum(Beta46)
}
InfBeta45=sum(Beta45,na.rm=T)
EndBeta45=SusBeta412+InfBeta45
EstBeta4=beta4-EndBeta43/EndBeta45
EstBeta4
}
##################################################################
################################# Delta #############################
################## susceptible period ####################
NewtonDelta=function(NewDelta){
S8=rep(0,time)
for(t in 1:time){
S7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
S7[i]=as.numeric(SumHnew1(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
S8[t]=sum(S7)
}
SusNew8=sum(S8)
###################### infectious period ###################
I10=rep(0,time)
for(t in 1:time){
I9=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXD2=c()
for(L in 1:nn){
SXD2[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
I9[i]=-as.numeric(SumHnew1(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean(SXD2))
}
}
}
}
I10[t]=sum(I9)
}
InfeNew10=sum(I10,na.rm=T)
EndNew10=SusNew8+InfeNew10
######################### Second Der...########################
S10=rep(0,time)
for(t in 1:time){
S9=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
S9[i]=-as.numeric(SumHnew2(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
S10[t]=sum(S9)
}
SusNew10=sum(S10)
###################### infectious period ###################
I12=rep(0,time)
for(t in 1:time){
I11=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SXD4=c()
for(L in 1:nn){
SXD4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
SXD6=c()
for(L in 1:nn){
SXD6[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
I11[i]=as.numeric(SumHnew2(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)*mean(SXD4))-as.numeric(SumHnew1(Nlabel,Di,EstAlpha,EstBeta1,EstBeta2,NewDelta,i,mmm,t,tau,lambda)^2*mean(SXD6))
}
}
}
}
I12[t]=sum(I11)
}
InfeNew12=sum(I12,na.rm=T)
EndNew12=SusNew10+InfeNew12
Estdelta1=NewDelta-EndNew10/EndNew12
diffDelta=Estdelta1-NewDelta
result=list(NewDelta=Estdelta1,diffDelta=diffDelta)
result
}
if(is.na(EstBeta4)){
Estdelta=NA
}
if(!is.na(EstBeta4)){
tdelta=1
Ndelta0=NewtonDelta(delta)
diffDelta=Ndelta0$diffDelta
NewDelta=Ndelta0$NewDelta
Estdelta=NewDelta
}
if(is.na(Estdelta)){
HatSigmmaU=NA
EstGammau=NA
MuxStarHat=NA
SigmaxStarHat=NA
MuxHat=NA
SigmaIndHat=NA
}
if(!is.na(Estdelta)){
##################################### Sigma_U #####################
##################################### Sigma_U #####################
##################################### Sigma_U #####################
##################################### Sigma_U ####################
Loglik11=function(par){
lambda1=par[[1]]
sigma1=par[[2]]
Log1=c()
for(L in 1:nn){
Log1[L]=dmvnorm(Pos[L,(mm+1):(2*mm)], rep(0,mm),sigma1^2*solve((lambda1*D+(1-lambda1)*I)), log = T)
}
LLL=-mean(Log1)
return(LLL)
}
init =c(lambda1,sigma1)
ml <- optim( init,Loglik11)
EstU1=ml$par
HatSigmmaU=EstU1[2]
EstGammau=EstU1[1]
#############################################################
#############################################################
MuxHat=0
SigmaIndHat=0
MuxStarHat=0
SigmaxStarHat=0
}
#############################################################
result=list(Pos1=Pos,beta1=EstBeta1,beta2=EstBeta2,beta3=EstBeta3,beta4=EstBeta4,alpha1=EstAlpha,delta=Estdelta,sigma1=HatSigmmaU,lambda1=EstGammau)
result
}
LogNaiv=function(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda){
nn=MHiteration
SumH=function(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda){
SumH1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
SumH1[j]=Di[i,j]^(-delta)
}
}
}
SumH1=replace(SumH1,is.infinite(SumH1),0)
SumH2=sum(SumH1)
SumH3=exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm])*SumH2
return(SumH3)
}
mean1L=function(Pos1,beta3,beta4,mmm,i){
d1=c()
for(L in 1:nn){
d1[L]=exp(beta3*Pos1[L,(2*mm+i)]+beta4*Pos1[L,mmm]+Pos1[L,mmm+mm])
}
SMean1=mean(d1)
return(SMean1)
}
mean2L=function(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos1[L,(2*mm+i)]+beta4*Pos1[L,mmm]+Pos1[L,(mmm+mm)])*dx)
if(prob11==0){SMean2=0}
if(prob11!=0){
SMean2=log(prob11)
}
return(SMean2)
}
A1=rep(0,time)
for(t in 1:time){
A2=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
A2[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1L(Pos1,beta3,beta4,mmm,i))
}
}
}
}
A1[t]=sum(A2)
}
SusA1=sum(A1)
###################### infectious period ###################
A3=rep(0,time)
for(t in 1:time){
A4=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
SA4=c()
for(L in 1:nn){
SA4[L]=mean2L(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
A4[i]=mean(SA4)
}
}
}
}
A3[t]=sum(A4)
}
InfA3=sum(A3,na.rm=T)
EndA3L=SusA1+InfA3
Log1=c()
for(L in 1:nn){
Log1[L]=dmvnorm(Pos1[L,(mm+1):(2*mm)], rep(0,mm), sigma1^2*solve((lambda1*D+(1-lambda1)*I)), log = T)
}
LLL=mean(Log1)
loglik1=LLL+EndA3L
return(loglik1)
}
##################################################################################
ObsInfNaiv=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,lambda){
nn=MHiteration
################################################################################################################
################################################################################################################
################################################################################################################
##################################################### Inf alpha ###########################################################
##################################################### Cov ###########################################################
alphaS=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
alphaS1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
alphaS1[t]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
alphaS[i,L]=sum(alphaS1)
}
}
alphaI=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
alphaI1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
alphaI1[t]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
alphaI[i,L]=sum(alphaI1)
}
}
alphaIS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
alphaIS[i,L]=alphaS[i,L]+alphaI[i,L]
}
}
SecondAlpha=c()
for(i in 1:n){
SecondAlpha[i]=mean(alphaIS[i,]^2)
}
FirstAlpha=c()
for(i in 1:n){
FirstAlpha[i]=mean(alphaIS[i,])^2
}
MAlpha=c()
for(i in 1:n){
MAlpha[i]=mean(alphaIS[i,])
}
##################################################################################
IA5=rep(0,time)
for(t in 1:time){
IA6=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISA6=c()
for(L in 1:nn){
ISA6[L]=-mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IA6[i]=mean(ISA6)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2
}
}
}
}
IA5[t]=sum(IA6)
}
IInfA5=sum(IA5,na.rm=T)
IEndA5=IInfA5+sum(MAlpha)
######################################
InfAlpha=-IEndA5-sum(SecondAlpha)+sum(FirstAlpha)
##################################################################################################################
####################################### Info beta1 ##############################
####################################### New beta1##############################
###############################Cov#######################################
Beta1S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta1S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta1S1[t]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta1S[i,L]=sum(Beta1S1)
}
}
###################### infectious period ###################
Beta1I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta1I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta1I1[t]=cov1[i]*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
Beta1I[i,L]=sum(Beta1I1)
}
}
Beta1IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta1IS[i,L]=Beta1S[i,L]+Beta1I[i,L]
}
}
SecondBeta1=c()
for(i in 1:n){
SecondBeta1[i]=mean(Beta1IS[i,]^2)
}
FirstBeta1=c()
for(i in 1:n){
FirstBeta1[i]=mean(Beta1IS[i,])^2
}
MBeta1=c()
for(i in 1:n){
MBeta1[i]=mean(Beta1IS[i,])
}
##########################################################################################
##########################################################################################
##########################################################################################
######################### Second Der...########################
##################### infectious period ###################
IBeta112=rep(0,time)
for(t in 1:time){
IBeta122=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta122[i]=-cov1[i]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta112[t]=sum(IBeta122)
}
ISusBeta112=sum(IBeta112)
IBeta15=rep(0,time)
for(t in 1:time){
IBeta16=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISB6=c()
for(L in 1:nn){
ISB6[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISB8=c()
for(L in 1:nn){
ISB8[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta16[i]=cov1[i]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISB6))-cov1[i]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISB8))
}
}
}
}
IBeta15[t]=sum(IBeta16)
}
IInfBeta15=sum(IBeta15,na.rm=T)
IEndBeta15=ISusBeta112+IInfBeta15
######################################
InfBeta1=-IEndBeta15-sum(SecondBeta1)+sum(FirstBeta1)
###########################################################################################
####################################### Info beta2 ##############################
#######################################Cov##############################
Beta2S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta2S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta2S1[t]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta2S[i,L]=sum(Beta2S1)
}
}
###################### infectious period ###################
Beta2I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta2I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta2I1[t]=cov2[mmm]*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)
}
}
}
}
Beta2I[i,L]=sum(Beta2I1)
}
}
Beta2IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta2IS[i,L]=Beta2S[i,L]+Beta2I[i,L]
}
}
SecondBeta2=c()
for(i in 1:n){
SecondBeta2[i]=mean(Beta2IS[i,]^2)
}
FirstBeta2=c()
for(i in 1:n){
FirstBeta2[i]=mean(Beta2IS[i,])^2
}
MBeta2=c()
for(i in 1:n){
MBeta2[i]=mean(Beta2IS[i,])
}
########################################################################################
########################################################################################
######################### Second Der...########################
##################### infectious period ###################
IBeta212=rep(0,time)
for(t in 1:time){
IBeta222=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta222[i]=-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta212[t]=sum(IBeta222)
}
ISusBeta212=sum(IBeta212)
IBeta25=rep(0,time)
for(t in 1:time){
IBeta26=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISB12=c()
for(L in 1:nn){
ISB12[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISB14=c()
for(L in 1:nn){
ISB14[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta26[i]=cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISB12))-cov2[mmm]^2*as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISB14))
}
}
}
}
IBeta25[t]=sum(IBeta26)
}
IInfBeta25=sum(IBeta25,na.rm=T)
IEndBeta25=ISusBeta212+IInfBeta25
######################################
InfBeta2=-IEndBeta25-sum(SecondBeta2)+sum(FirstBeta2)
###########################################################################################
####################################### Info beta3 ##############################
####################################### Cov##############################
Beta3S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta3S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta3S1[t]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta3S[i,L]=sum(Beta3S1)
}
}
###################### infectious period ###################
Beta3I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta3I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta3I1[t]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Beta3I[i,L]=sum(Beta3I1)
}
}
Beta3IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta3IS[i,L]=Beta3S[i,L]+Beta3I[i,L]
}
}
SecondBeta3=c()
for(i in 1:n){
SecondBeta3[i]=mean(Beta3IS[i,]^2)
}
FirstBeta3=c()
for(i in 1:n){
FirstBeta3[i]=mean(Beta3IS[i,])^2
}
MBeta3=c()
for(i in 1:n){
MBeta3[i]=mean(Beta3IS[i,])
}
###############################################################################################
###############################################################################################
#################################beta4##################################
##################### infectious period ###################
IBeta312=rep(0,time)
for(t in 1:time){
IBeta322=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta322[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX3(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta312[t]=sum(IBeta322)
}
ISusBeta312=sum(IBeta312)
IBeta35=rep(0,time)
for(t in 1:time){
IBeta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISXB316=c()
for(L in 1:nn){
ISXB316[L]=meanX4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISXB315=c()
for(L in 1:nn){
ISXB315[L]=meanX5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta36[i]=as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISXB316))-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISXB315))
}
}
}
}
IBeta35[t]=sum(IBeta36)
}
IInfBeta35=sum(IBeta35,na.rm=T)
IEndBeta35=ISusBeta312+IInfBeta35
######################################
InfBeta3=-IEndBeta35-sum(SecondBeta3)+sum(FirstBeta3)
###########################################################################################
###########################################################################################
####################################### Info beta4 ##############################
####################################### Cov##############################
Beta4S=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta4S1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Beta4S1[t]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Beta4S[i,L]=sum(Beta4S1)
}
}
###################### infectious period ###################
Beta4I=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta4I1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Beta4I1[t]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Beta4I[i,L]=sum(Beta4I1)
}
}
Beta4IS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
Beta4IS[i,L]=Beta4S[i,L]+Beta4I[i,L]
}
}
SecondBeta4=c()
for(i in 1:n){
SecondBeta4[i]=mean(Beta4IS[i,]^2)
}
FirstBeta4=c()
for(i in 1:n){
FirstBeta4[i]=mean(Beta4IS[i,])^2
}
MBeta4=c()
for(i in 1:n){
MBeta4[i]=mean(Beta4IS[i,])
}
###############################################################################################
###############################################################################################
#################################beta4##################################
##################### infectious period ###################
IBeta412=rep(0,time)
for(t in 1:time){
IBeta422=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IBeta422[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar3(Pos,beta3,beta4,mmm,i))
}
}
}
}
IBeta412[t]=sum(IBeta422)
}
ISusBeta412=sum(IBeta412)
IBeta45=rep(0,time)
for(t in 1:time){
IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISXB4=c()
for(L in 1:nn){
ISXB4[L]=meanXstar4(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISXB5=c()
for(L in 1:nn){
ISXB5[L]=meanXstar5(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IBeta46[i]=as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISXB4))-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISXB5))
}
}
}
}
IBeta45[t]=sum(IBeta46)
}
IInfBeta45=sum(IBeta45,na.rm=T)
IEndBeta45=ISusBeta412+IInfBeta45
######################################
InfBeta4=-IEndBeta45-sum(SecondBeta4)+sum(FirstBeta4)
###########################################################################################
################################################# Info Delta #####################################
#################################Cov #############################
DeltaS=matrix(NA,n,nn)
for(i in 1:n){
for(L in 1:nn){
DeltaS1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
DeltaS1[t]=SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
DeltaS[i,L]=sum(DeltaS1)
}
}
###################### infectious period ###################
DeltaI=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
DeltaI1=rep(0,time)
for(t in 1:time){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
DeltaI1[t]=-SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
DeltaI[i,L]=sum(DeltaI1)
}
}
DeltaIS=matrix(0,n,nn)
for(i in 1:n){
for(L in 1:nn){
DeltaIS[i,L]=DeltaS[i,L]+DeltaI[i,L]
}
}
SecondDelta=c()
for(i in 1:n){
SecondDelta[i]=mean(DeltaIS[i,]^2)
}
FirstDelta=c()
for(i in 1:n){
FirstDelta[i]=mean(DeltaIS[i,])^2
}
MDelta=c()
for(i in 1:n){
MDelta[i]=mean(DeltaIS[i,])
}
############################################################################################################
############################################################################################################
######################### Second Der...########################
IS10=rep(0,time)
for(t in 1:time){
IS9=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
IS9[i]=-as.numeric(SumHnew2(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean1(Pos,beta3,beta4,mmm,i))
}
}
}
}
IS10[t]=sum(IS9)
}
ISusNew10=sum(IS10)
###################### infectious period ###################
II12=rep(0,time)
for(t in 1:time){
II11=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
ISXD4=c()
for(L in 1:nn){
ISXD4[L]=mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
ISXD6=c()
for(L in 1:nn){
ISXD6[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
II11[i]=as.numeric(SumHnew2(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean(ISXD4))-as.numeric(SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(ISXD6))
}
}
}
}
II12[t]=sum(II11)
}
IInfeNew12=sum(II12,na.rm=T)
IEndNew12=ISusNew10+IInfeNew12
######################################
InfDelta=-IEndNew12-sum(SecondDelta)+sum(FirstDelta)
###########################################################################################
###########################################################################################
###########################################################################################
###########################################Inf alpha & beta1################################################
IAlphaBeta1=rep(0,time)
for(t in 1:time){
IAlphaBeta11=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAB1=c()
for(L in 1:nn){
IAB1[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta11[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IAB1)
}
}
}
}
IAlphaBeta1[t]=sum(IAlphaBeta11)
}
DeriveAB1=sum(IAlphaBeta1,na.rm=T)+sum(MBeta1)
AlphaBeta1=c()
for(i in 1:n){
AlphaBeta1[i]=mean(alphaIS[i,]*Beta1IS[i,])
}
InfAlBeta1=-DeriveAB1-sum(AlphaBeta1)+sum(MAlpha*MBeta1)
###########################################Inf alpha & beta2################################################
IAlphaBeta2=rep(0,time)
for(t in 1:time){
IAlphaBeta21=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAB2=c()
for(L in 1:nn){
IAB2[L]=mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta21[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IAB2)
}
}
}
}
IAlphaBeta2[t]=sum(IAlphaBeta21)
}
DeriveAB2=sum(IAlphaBeta2,na.rm=T)+sum(MBeta2)
AlphaBeta2=c()
for(i in 1:n){
AlphaBeta2[i]=mean(alphaIS[i,]*Beta2IS[i,])
}
InfAlBeta2=-DeriveAB2-sum(AlphaBeta2)+sum(MAlpha*MBeta2)
###########################################Inf alpha & beta3################################################
meanX6=function(Nlabel,Pos,Di,alpha1,beta1,beta3,beta2,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX6=0}
if(prob11!=0){
SMeanX6=Pos[L,(2*mm+i)]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanX6)
}
IAlphaBeta3=rep(0,time)
for(t in 1:time){
IAlphaBeta31=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IABx5=c()
for(L in 1:nn){
IABx5[L]=meanX6(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta31[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IABx5))
}
}
}
}
IAlphaBeta3[t]=sum(IAlphaBeta31)
}
DeriveAB3=sum(IAlphaBeta3,na.rm=T)+sum(MBeta3)
AlphaBeta3=c()
for(i in 1:n){
AlphaBeta3[i]=mean(alphaIS[i,]*Beta3IS[i,])
}
InfAlBeta3=-DeriveAB3-sum(AlphaBeta3)+sum(MAlpha*MBeta3)
###########################################Inf alpha & beta4################################################
meanXstar6=function(Nlabel,Pos,Di,alpha1,beta1,beta3,beta2,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMean6=0}
if(prob11!=0){
SMean6=Pos[L,mmm]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMean6)
}
IAlphaBeta4=rep(0,time)
for(t in 1:time){
IAlphaBeta41=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAB5=c()
for(L in 1:nn){
IAB5[L]=meanXstar6(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
IAlphaBeta41[i]=-as.numeric(SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean(IAB5))
}
}
}
}
IAlphaBeta4[t]=sum(IAlphaBeta41)
}
DeriveAB4=sum(IAlphaBeta4,na.rm=T)+sum(MBeta4)
AlphaBeta4=c()
for(i in 1:n){
AlphaBeta4[i]=mean(alphaIS[i,]*Beta4IS[i,])
}
InfAlBeta4=-DeriveAB4-sum(AlphaBeta4)+sum(MAlpha*MBeta4)
###########################################Inf alpha & delta ################################################
IAlphaDelta1=c()
for(L in 1:nn){
IAlphaDelta2=rep(0,time)
for(t in 1:time){
IAlphaDelta3=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IAlphaDelta3[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IAlphaDelta2[t]=sum(IAlphaDelta3)
}
IAlphaDelta1[L]=sum(IAlphaDelta2,na.rm=T)
}
DeriveAD=mean(IAlphaDelta1)+sum(MDelta)
AlphaDelta=c()
for(i in 1:n){
AlphaDelta[i]=mean(alphaIS[i,]*DeltaIS[i,])
}
InfAlDelta=-DeriveAD-sum(AlphaDelta)+sum(MAlpha*MDelta)
###########################################Inf beta1 & delta ################################################
Delta18=c()
for(L in 1:nn){
Delta8=rep(0,time)
for(t in 1:time){
Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
Delta7[i]=cov1[i]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
Delta8[t]=sum(Delta7)
}
Delta18[L]=sum(Delta8)
}
###################### infectious period ###################
Delta10=c()
for(L in 1:nn){
Delta11=rep(0,time)
for(t in 1:time){
Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Delta12[i]=-cov1[i]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Delta11[t]=sum(Delta12)
}
Delta10[L]=sum(Delta11,na.rm=T)
}
DeltaEnd=c()
for(L in 1:nn){
DeltaEnd[L]=Delta18[L]+Delta10[L]
}
Delta15=c()
for(L in 1:nn){
Delta16=rep(0,time)
for(t in 1:time){
Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
Delta17[i]=cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
Delta16[t]=sum(Delta17,na.rm=T)
}
Delta15[L]=sum(Delta16,na.rm=T)
}
DeriveBD=mean(Delta15)+mean(DeltaEnd)
Beta1Delta=c()
for(i in 1:n){
Beta1Delta[i]=mean(Beta1IS[i,]*DeltaIS[i,])
}
InfBeta1Delta=-DeriveBD-sum(Beta1Delta)+sum(MBeta1*MDelta)
###########################################Inf beta2 & delta ################################################
B2Delta18=c()
for(L in 1:nn){
B2Delta8=rep(0,time)
for(t in 1:time){
B2Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B2Delta7[i]=cov2[mmm]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B2Delta8[t]=sum(B2Delta7)
}
B2Delta18[L]=sum(B2Delta8)
}
###################### infectious period ###################
B2Delta10=c()
for(L in 1:nn){
B2Delta11=rep(0,time)
for(t in 1:time){
B2Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2Delta12[i]=-cov2[mmm]*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2Delta11[t]=sum(B2Delta12)
}
B2Delta10[L]=sum(B2Delta11,na.rm=T)
}
B2DeltaEnd=c()
for(L in 1:nn){
B2DeltaEnd[L]=B2Delta18[L]+B2Delta10[L]
}
B2Delta15=c()
for(L in 1:nn){
B2Delta16=rep(0,time)
for(t in 1:time){
B2Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2Delta17[i]=cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2Delta16[t]=sum(B2Delta17)
}
B2Delta15[L]=sum(B2Delta16,na.rm=T)
}
DeriveB2D=mean(B2Delta15)+mean(B2DeltaEnd)
Beta2Delta=c()
for(i in 1:n){
Beta2Delta[i]=mean(Beta2IS[i,]*DeltaIS[i,])
}
InfBeta2Delta=-DeriveB2D-sum(Beta2Delta)+sum(MBeta2*MDelta)
###########################################Inf beta3& delta ################################################
B3Delta18=c()
for(L in 1:nn){
B3Delta8=rep(0,time)
for(t in 1:time){
B3Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B3Delta7[i]=SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B3Delta8[t]=sum(B3Delta7)
}
B3Delta18[L]=sum(B3Delta8)
}
###################### infectious period ###################
meanX7=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanX7=0}
if(prob11!=0){
SMeanX7=Pos[L,(2*mm+i)]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanX7)
}
B3Delta10=c()
for(L in 1:nn){
B3Delta11=rep(0,time)
for(t in 1:time){
B3Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3Delta12[i]=-SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3Delta11[t]=sum(B3Delta12)
}
B3Delta10[L]=sum(B3Delta11,na.rm=T)
}
B3DeltaEnd=c()
for(L in 1:nn){
B3DeltaEnd[L]=B3Delta18[L]+B3Delta10[L]
}
B3Delta15=c()
for(L in 1:nn){
B3Delta16=rep(0,time)
for(t in 1:time){
B3Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3Delta17[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3Delta16[t]=sum(B3Delta17)
}
B3Delta15[L]=sum(B3Delta16,na.rm=T)
}
DeriveB3D=mean(B3Delta15)+mean(B3DeltaEnd)
Beta3Delta=c()
for(i in 1:n){
Beta3Delta[i]=mean(Beta3IS[i,]*DeltaIS[i,])
}
InfBeta3Delta=-DeriveB3D-sum(Beta3Delta)+sum(MBeta3*MDelta)
###########################################Inf beta4& delta ################################################
B4Delta18=c()
for(L in 1:nn){
B4Delta8=rep(0,time)
for(t in 1:time){
B4Delta7=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B4Delta7[i]=SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B4Delta8[t]=sum(B4Delta7)
}
B4Delta18[L]=sum(B4Delta8)
}
###################### infectious period ###################
meanXstar7=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXstar7=0}
if(prob11!=0){
SMeanXstar7=Pos[L,mmm]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanXstar7)
}
B4Delta10=c()
for(L in 1:nn){
B4Delta11=rep(0,time)
for(t in 1:time){
B4Delta12=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B4Delta12[i]=-SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B4Delta11[t]=sum(B4Delta12)
}
B4Delta10[L]=sum(B4Delta11,na.rm=T)
}
B4DeltaEnd=c()
for(L in 1:nn){
B4DeltaEnd[L]=B4Delta18[L]+B4Delta10[L]
}
B4Delta15=c()
for(L in 1:nn){
B4Delta16=rep(0,time)
for(t in 1:time){
B4Delta17=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B4Delta17[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*SumHnew1(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B4Delta16[t]=sum(B4Delta17)
}
B4Delta15[L]=sum(B4Delta16,na.rm=T)
}
DeriveB4D=mean(B4Delta15)+mean(B4DeltaEnd)
Beta4Delta=c()
for(i in 1:n){
Beta4Delta[i]=mean(Beta4IS[i,]*DeltaIS[i,])
}
InfBeta4Delta=-DeriveB4D-sum(Beta4Delta)+sum(MBeta4*MDelta)
########################################### beta1 & beta 2 ################################################################
B1Beta21=c()
for(L in 1:nn){
B1NewBeta21=rep(0,time)
for(t in 1:time){
B1NewBeta22=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B1NewBeta22[i]=-cov1[i]*cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B1NewBeta21[t]=sum(B1NewBeta22)
}
B1Beta21[L]=sum(B1NewBeta21)
}
###################### infectious period ###################
B1InfBeta23=c()
for(L in 1:nn){
B1NewBeta23=rep(0,time)
for(t in 1:time){
B1NewBeta24=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B1NewBeta24[i]=cov1[i]*cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*mean2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B1NewBeta23[t]=sum(B1NewBeta24)
}
B1InfBeta23[L]=sum(B1NewBeta23,na.rm=T)
}
New23Beta=c()
for(L in 1:nn){
New23Beta[L]=B1Beta21[L]+B1InfBeta23[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta1Beat2=c()
for(L in 1:nn){
IBeta25=rep(0,time)
for(t in 1:time){
IBeta26=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IBeta26[i]=-cov1[i]*cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*mean3(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IBeta25[t]=sum(IBeta26)
}
Beta1Beat2[L]=sum(IBeta25,na.rm=T)
}
DeriveBeta1Beat2=mean(Beta1Beat2)+mean(New23Beta)
Beta1Beat21=c()
for(i in 1:n){
Beta1Beat21[i]=mean(Beta1IS[i,]*Beta2IS[i,])
}
InfBeta1Beat2=-DeriveBeta1Beat2-sum(Beta1Beat21)+sum(MBeta1*MBeta2)
########################################### beta1 & beta 3 ################################################################
B1Bet1a31=c()
for(L in 1:nn){
B1NewBeta31=rep(0,time)
for(t in 1:time){
B1NewBeta32=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B1NewBeta32[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B1NewBeta31[t]=sum(B1NewBeta32)
}
B1Bet1a31[L]=sum(B1NewBeta31)
}
###################### infectious period ###################
B1NewInfBeta33=c()
for(L in 1:nn){
B1NewBeta33=rep(0,time)
for(t in 1:time){
B1NewBeta34=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B1NewBeta34[i]=cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B1NewBeta33[t]=sum(B1NewBeta34)
}
B1NewInfBeta33[L]=sum(B1NewBeta33,na.rm=T)
}
B1EndBeta33=c()
for(L in 1:nn){
B1EndBeta33[L]=B1Bet1a31[L]+B1NewInfBeta33[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta1Beta3=c()
for(L in 1:nn){
IBeta35=rep(0,time)
for(t in 1:time){
IBeta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IBeta36[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IBeta35[t]=sum(IBeta36)
}
Beta1Beta3[L]=sum(IBeta35,na.rm=T)
}
DeriveBeta1Beta3=mean(Beta1Beta3)+mean(B1EndBeta33)
Beta1Beat31=c()
for(i in 1:n){
Beta1Beat31[i]=mean(Beta1IS[i,]*Beta3IS[i,])
}
InfBeta3Beta1=-DeriveBeta1Beta3-sum(Beta1Beat31)+sum(MBeta1*MBeta3)
########################################### beta1 & beta 4 ################################################################
B1Bet1a41=c()
for(L in 1:nn){
B1NewBeta41=rep(0,time)
for(t in 1:time){
B1NewBeta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B1NewBeta42[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B1NewBeta41[t]=sum(B1NewBeta42)
}
B1Bet1a41[L]=sum(B1NewBeta41)
}
###################### infectious period ###################
B1NewInfBeta43=c()
for(L in 1:nn){
B1NewBeta43=rep(0,time)
for(t in 1:time){
B1NewBeta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B1NewBeta44[i]=cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B1NewBeta43[t]=sum(B1NewBeta44)
}
B1NewInfBeta43[L]=sum(B1NewBeta43,na.rm=T)
}
B1EndBeta43=c()
for(L in 1:nn){
B1EndBeta43[L]=B1Bet1a41[L]+B1NewInfBeta43[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta1Beta4=c()
for(L in 1:nn){
IBeta45=rep(0,time)
for(t in 1:time){
IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
IBeta46[i]=-cov1[i]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanXstar7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
IBeta45[t]=sum(IBeta46)
}
Beta1Beta4[L]=sum(IBeta45,na.rm=T)
}
DeriveBeta1Beta4=mean(Beta1Beta4)+mean(B1EndBeta43)
Beta1Beat41=c()
for(i in 1:n){
Beta1Beat41[i]=mean(Beta1IS[i,]*Beta4IS[i,])
}
InfBeta4Beta1=-DeriveBeta1Beta4-sum(Beta1Beat41)+sum(MBeta1*MBeta4)
########################################### beta2 & beta 3 ################################################################
B2Beta31=c()
for(L in 1:nn){
B2NewBeta31=rep(0,time)
for(t in 1:time){
B2NewBeta32=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B2NewBeta32[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B2NewBeta31[t]=sum(B2NewBeta32)
}
B2Beta31[L]=sum(B2NewBeta31)
}
###################### infectious period ###################
B2NewInfBeta33=c()
for(L in 1:nn){
B2NewBeta33=rep(0,time)
for(t in 1:time){
B2NewBeta34=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2NewBeta34[i]=cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2NewBeta33[t]=sum(B2NewBeta34)
}
B2NewInfBeta33[L]=sum(B2NewBeta33,na.rm=T)
}
B2EndBeta33=c()
for(L in 1:nn){
B2EndBeta33[L]=B2Beta31[L]+B2NewInfBeta33[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta2Beta3=c()
for(L in 1:nn){
B2IBeta35=rep(0,time)
for(t in 1:time){
B2IBeta36=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2IBeta36[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2IBeta35[t]=sum(B2IBeta36)
}
Beta2Beta3[L]=sum(B2IBeta35,na.rm=T)
}
DeriveBeta2Beta3=mean(Beta2Beta3)+mean(B2EndBeta33)
Beta2Beat31=c()
for(i in 1:n){
Beta2Beat31[i]=mean(Beta2IS[i,]*Beta3IS[i,])
}
InfBeta3Beta2=-DeriveBeta2Beta3-sum(Beta2Beat31)+sum(MBeta2*MBeta3)
########################################### beta2 & beta 4 ################################################################
B2Beta41=c()
for(L in 1:nn){
B2NewBeta41=rep(0,time)
for(t in 1:time){
B2NewBeta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B2NewBeta42[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B2NewBeta41[t]=sum(B2NewBeta42)
}
B2Beta41[L]=sum(B2NewBeta41)
}
###################### infectious period ###################
B2NewInfBeta43=c()
for(L in 1:nn){
B2NewBeta43=rep(0,time)
for(t in 1:time){
B2NewBeta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2NewBeta44[i]=cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXstar2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2NewBeta43[t]=sum(B2NewBeta44)
}
B2NewInfBeta43[L]=sum(B2NewBeta43,na.rm=T)
}
B2EndBeta43=c()
for(L in 1:nn){
B2EndBeta43[L]=B2Beta41[L]+B2NewInfBeta43[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta2Beta4=c()
for(L in 1:nn){
B2IBeta45=rep(0,time)
for(t in 1:time){
B2IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B2IBeta46[i]=-cov2[mmm]*SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanXstar7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B2IBeta45[t]=sum(B2IBeta46)
}
Beta2Beta4[L]=sum(B2IBeta45,na.rm=T)
}
DeriveBeta2Beta4=mean(Beta2Beta4)+mean(B2EndBeta43)
Beta2Beat41=c()
for(i in 1:n){
Beta2Beat41[i]=mean(Beta2IS[i,]*Beta4IS[i,])
}
InfBeta4Beta2=-DeriveBeta2Beta4-sum(Beta2Beat41)+sum(MBeta2*MBeta4)
#######################################################################################################
########################################### beta3 & beta 4 ################################################################
B3Beta41=c()
for(L in 1:nn){
B3NewBeta41=rep(0,time)
for(t in 1:time){
B3NewBeta42=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if (tau[i]>(t+1)|tau[i]== 0){
B3NewBeta42[i]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*Pos[L,mmm]*Pos[L,(2*mm+i)]*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
}
}
}
B3NewBeta41[t]=sum(B3NewBeta42)
}
B3Beta41[L]=sum(B3NewBeta41)
}
###################### infectious period ###################
meanXX2=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXX2=0}
if(prob11!=0){
SMeanXX2=Pos[L,(2*mm+i)]*Pos[L,mmm]*(1-prob11)/prob11*exp(beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])
}
return(SMeanXX2)
}
meanXX7=function(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta)
}
}
}
dx1=replace(dx1,is.infinite(dx1),0)
dx=sum(dx1)
prob11=1-exp(-exp(alpha1+beta1*cov1[i]+beta2*cov2[mmm]+beta3*Pos[L,(2*mm+i)]+beta4*Pos[L,mmm]+Pos[L,mmm+mm])*dx)
if (is.na(prob11)) {
prob11 <- 0
}
if(prob11==0){SMeanXX7=0}
if(prob11!=0){
SMeanXX7=Pos[L,(2*mm+i)]*Pos[L,mmm]*(1-prob11)/prob11^2*exp(2*beta3*Pos[L,(2*mm+i)]+2*beta4*Pos[L,mmm]+2*Pos[L,mmm+mm])
}
return(SMeanXX7)
}
B3NewInfBeta43=c()
for(L in 1:nn){
B3NewBeta43=rep(0,time)
for(t in 1:time){
B3NewBeta44=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if(Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3NewBeta44[i]=SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)*meanXX2(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3NewBeta43[t]=sum(B3NewBeta44)
}
B3NewInfBeta43[L]=sum(B3NewBeta43,na.rm=T)
}
B3EndBeta43=c()
for(L in 1:nn){
B3EndBeta43[L]=B3Beta41[L]+B3NewInfBeta43[L]
}
######################### Second Der...########################
##################### infectious period ###################
Beta3Beta4=c()
for(L in 1:nn){
B3IBeta45=rep(0,time)
for(t in 1:time){
B3IBeta46=rep(0,n)
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]==(t+1)){
B3IBeta46[i]=-SumH(Nlabel,Di,alpha1,beta1,beta2,delta,i,mmm,t,tau,lambda)^2*meanXX7(Nlabel,Pos,Di,alpha1,beta1,beta2,beta3,beta4,delta,mmm,i,t,L,tau,lambda)
}
}
}
}
B3IBeta45[t]=sum(B3IBeta46)
}
Beta3Beta4[L]=sum(B3IBeta45,na.rm=T)
}
DeriveBeta3Beta4=mean(Beta3Beta4)+mean(B3EndBeta43)
Beta3Beat41=c()
for(i in 1:n){
Beta3Beat41[i]=mean(Beta3IS[i,]*Beta4IS[i,])
}
InfBeta3Beta4=-DeriveBeta3Beta4-sum(Beta3Beat41)+sum(MBeta3*MBeta4)
A1=c(InfAlpha,InfAlBeta1,InfAlBeta2,InfAlBeta3,InfAlBeta4,InfAlDelta)
A2=c(InfAlBeta1,InfBeta1,InfBeta1Beat2,InfBeta3Beta1,InfBeta4Beta1,InfBeta1Delta)
A3=c(InfAlBeta2,InfBeta1Beat2,InfBeta2,InfBeta3Beta2,InfBeta4Beta2,InfBeta2Delta)
A4=c(InfAlBeta3,InfBeta3Beta1,InfBeta3Beta2,InfBeta3,InfBeta3Beta4,InfBeta3Delta)
A5=c(InfAlBeta4,InfBeta4Beta1,InfBeta4Beta2,InfBeta3Beta4,InfBeta4,InfBeta4Delta)
A6=c(InfAlDelta,InfBeta1Delta,InfBeta2Delta,InfBeta3Delta,InfBeta4Delta,InfDelta)
ObservedInf=rbind(A1,A2,A3,A4,A5,A6)
Variances=diag(solve(ObservedInf))
Variances
CInfAlpha=-IEndA5
CInfBeta1=-IEndBeta15
CInfBeta2=-IEndBeta25
CInfBeta3=-IEndBeta35
CInfBeta4=-IEndBeta45
CInfDelta=-IEndNew12
CInfAlBeta1=-DeriveAB1
CInfAlBeta2=-DeriveAB2
CInfAlBeta3=-DeriveAB3
CInfAlBeta4=-DeriveAB4
CInfAlDelta=-DeriveAD
CInfBeta1Delta=-DeriveBD
CInfBeta2Delta=-DeriveB2D
CInfBeta3Delta=-DeriveB3D
CInfBeta4Delta=-DeriveB4D
CInfBeta1Beat2=-DeriveBeta1Beat2
CInfBeta3Beta1=-DeriveBeta1Beta3
CInfBeta4Beta1=-DeriveBeta1Beta4
CInfBeta3Beta2=-DeriveBeta2Beta3
CInfBeta4Beta2=-DeriveBeta2Beta4
CInfBeta3Beta4=-DeriveBeta3Beta4
CA1=c(CInfAlpha,CInfAlBeta1,CInfAlBeta2,CInfAlBeta3,CInfAlBeta4,CInfAlDelta)
CA2=c(CInfAlBeta1,CInfBeta1,CInfBeta1Beat2,CInfBeta3Beta1,CInfBeta4Beta1,CInfBeta1Delta)
CA3=c(CInfAlBeta2,CInfBeta1Beat2,CInfBeta2,CInfBeta3Beta2,CInfBeta4Beta2,CInfBeta2Delta)
CA4=c(CInfAlBeta3,CInfBeta3Beta1,CInfBeta3Beta2,CInfBeta3,CInfBeta3Beta4,CInfBeta3Delta)
CA5=c(CInfAlBeta4,CInfBeta4Beta1,CInfBeta4Beta2,CInfBeta3Beta4,CInfBeta4,CInfBeta4Delta)
CA6=c(CInfAlDelta,CInfBeta1Delta,CInfBeta2Delta,CInfBeta3Delta,CInfBeta4Delta,CInfDelta)
CObservedInf=rbind(CA1,CA2,CA3,CA4,CA5,CA6)
CVariances=diag(solve(CObservedInf))
CVariances
######################################Spatial parameters##########################################
QLoglik11=function(par){
sigma1=par[[1]]
lambda1=par[[2]]
Log1=c()
for(L in 1:nn){
Log1[L]=dmvnorm(Pos[L,(mm+1):(2*mm)], rep(0,mm), sigma1^2*solve((lambda1*D+(1-lambda1)*I)), log = T)
}
LLL=mean(Log1)
return(LLL)
}
Hes=hessian(QLoglik11,c(sigma1,lambda1))
VarSpatial=diag(solve(-Hes))
result=list(CVariances=CVariances,VarSpatial=VarSpatial,ObservedInf=ObservedInf,Variances=Variances)
result
}
#######################Data Generation and Results################
######################################################
#start of loop for simulation
CovMEA=matrix(0,ITER,mm)
CovMEInd=matrix(0,ITER,n)
GePHI=matrix(0,ITER,mm)
for(iter in 1:ITER){
I=diag(mm)
mu=rep(0,mm)
Sigma0=sigma0^2*solve((lambda0*D+(1-lambda0)*I))
det(Sigma0)
GePHI[iter,]=mvrnorm(1, mu, Sigma0, tol = 1e-6)
############################################################
###########################
x=data[,1,iter]
y=data[,2,iter]
########################
Di=matrix(0,n,n)
for(i in 1:n){
for(j in 1:n){
Di[i,j]=sqrt((x[i]-x[j])^2+(y[i]-y[j])^2)
}
}
Di=Di*100
##########
vv=CovXStar1
ww=CovX
phi=GePHI[iter,]
for(t in 1:time){
for(i in 1:n){
for(mmm in 1:mm){
if (Nlabel[i]==mmm){
if(tau[i]== 0){
dx1=rep(0,n)
for(j in 1:n){
if (Newlabel[j,mmm]!=0){
if(tau[j]<=t & (tau[j]+lambda[j])>t & tau[j]!=0){
dx1[j]=Di[i,j]^(-delta0)
}
}
}
dx=sum(dx1)
P=1-exp(-exp(alpha0+beta10*cov1[i]+beta20*cov2[mmm]+beta30*CovX[i]+beta40*CovXStar1[mmm]+phi[mmm])*dx)
u=runif(1,0,1)
if(P>u){
tau[i]=t+1
}
}
}
}
}
}
tau
####################################################################################
####################################################################################
LA=c()
ss=1
est0=estfunNaiv(Nlabel,phi,Di,alpha0,beta10,beta20,beta30,beta40,delta0,sigma0,lambda0,D,lambda)
alpha1=est0$alpha1
delta=est0$delta
lambda1=est0$lambda1
sigma1=est0$sigma1
beta1=est0$beta1
beta2=est0$beta2
beta3=est0$beta3
beta4=est0$beta4
Pos1=est0$Pos1
if(is.na(alpha1)|is.na(delta)|is.na(lambda1)|is.na(sigma1)|is.na(beta1)|is.na(beta2)|is.na(beta3)|is.na(beta4)){
LA[1]=NA
}
if(!is.na(alpha1)&&!is.na(delta)&&!is.na(lambda1)&&!is.na(sigma1)&&!is.na(beta1)&&!is.na(beta2)&&!is.na(beta3)&&!is.na(beta4)){
LA[1]=LogNaiv(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda)
}
repeat{
ss=ss+1
if(is.na(LA[1])){
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=NA)
break
}
if(ss>25){
alpha1=NA
delta=NA
sigma1=NA
lambda1=NA
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=NA)
break
}
if(!is.na(alpha1)&&!is.na(delta)&&!is.na(lambda1)&&!is.na(sigma1)&&!is.na(beta1)&&!is.na(beta2)&&!is.na(beta3)&&!is.na(beta4)){
if(sigma1<0 |lambda1>1|lambda1<0|delta<0){
alpha1=NA
delta=NA
sigma1=NA
lambda1=NA
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=ss)
break
}
}
E0=c(alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1)
LA
est=estfunNaiv(Nlabel,phi,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda)
alpha1=est$alpha1
delta=est$delta
lambda1=est$lambda1
sigma1=est$sigma1
beta1=est$beta1
beta2=est$beta2
beta3=est$beta3
beta4=est$beta4
Pos1=est$Pos1
if(!is.na(alpha1)&&!is.na(delta)&&!is.na(lambda1)&&!is.na(sigma1)&&!is.na(beta1)&&!is.na(beta2)&&!is.na(beta3)&&!is.na(beta4)){
if(sigma1<0 |lambda1>1|lambda1<0|delta<0){
alpha1=NA
delta=NA
sigma1=NA
lambda1=NA
out1=list(alpha1=NA,delta=NA,sigma1=NA,lambda1=NA,beta1=NA,ss=ss)
break
}
if(sigma1>=0 & lambda1<=1 & lambda1>=0){
E1=c(alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1)
Dist=sqrt(sum((E0-E1)^2))
LA[ss]=LogNaiv(Nlabel,Pos1,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,D,lambda)
out1=list(LA=LA,Pos1=Pos1,alpha1=alpha1,beta1=beta1,beta2=beta2,beta3=beta3,beta4=beta4,delta=delta,sigma1=sigma1,lambda1=lambda1,ss=ss,E1=E1,E0=E0)
if(!abs((LA[ss]-LA[ss-1])/LA[ss])>eps){
break
}
}
}
if(is.na(alpha1)|is.na(delta)|is.na(lambda1)|is.na(sigma1)|is.na(beta1)|is.na(beta2)|is.na(beta3)|is.na(beta4)){
out1=list(alpha1=NA,beta1=NA,beta2=NA,beta3=NA,beta4=NA,delta=NA,sigma1=NA,lambda1=NA)
break
}
}
NaivPos=Pos1
NaivEstpar=c(alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1)
NaivFinalInf=ObsInfNaiv(Nlabel,NaivPos,Di,alpha1,beta1,beta2,beta3,beta4,delta,sigma1,lambda1,lambda)
if(is.na(sigma1)){
NaivSimPAR[iter,]=NA
NaivSimVarPar[iter,]=NA
NaivCSimVarPar[iter,]=NA
NaivSimInfPar[iter,]=NA
NaivSimVarSpatial[iter,]=NA
NaivSimPos[[iter]]=NA
}
if(!is.na(sigma1)){
NaivSimPAR[iter,]=NaivEstpar
NaivSimVarPar[iter,]=NaivFinalInf$Variances
NaivSimInfPar[iter,]=diag(NaivFinalInf$ObservedInf)
NaivSimVarSpatial[iter,]=(NaivFinalInf$VarSpatial)
NaivSimPos[[iter]]=NaivPos
NaivCSimVarPar[iter,]=NaivFinalInf$CVariances
}
}
result=list(NaivSimPAR=NaivSimPAR,NaivSimVarPar=NaivSimVarPar,NaivSimVarSpatial=NaivSimVarSpatial,NaivSimPos=NaivSimPos,NaivCSimVarPar=NaivCSimVarPar)
}
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