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#c9
#' Edition 2 Gradient-function for Coyne et al's rabies model
#' @param t Implicit argument for time
#' @param logx A vector with values for the log-states
#' @param parms A vector with parameter values for the dynamical system
#' @return A list of gradients for the log system
#' @examples
#' require(deSolve)
#' times = seq(0, 50, by=1/520)
#' paras = c(gamma = 0.0397, b = 0.836, a = 1.34, sigma = 7.5,
#' alpha = 66.36, beta = 33.25, c = 0, rho = 0.8)
#' start = log(c(S=12.69/2, E1=0.1, E2=0.1, I = 0.1, R = 0.1))
#' out = as.data.frame(ode(start, times, coyne, paras))
#' @export
coyne2 = function(t, logx, parms){
x = exp(logx)
S = x[1]
E1 = x[2]
E2 = x[3]
I = x[4]
R = x[5]
N = sum(x)
with(as.list(parms),{
dS = a * (S + R) - beta * S * I -
d * N * S - (b + c) * S
dE1= lambda * beta * S * I - d * N * E1 -
(b + sigma + c) * E1
dE2= (1-lambda) * beta * S * I - d * N * E2 -
(b + sigma + c) * E2
dI = sigma * E1 - d * N * I -
(b + alpha + c) * I
dR = sigma * E2 - d * N * R - (b + c) * R
res = c(dS/S, dE1/E1, dE2/E2, dI/I, dR/R)
list(res)
})
}
#' Edition 1 Gradient-function for Coyne et al's rabies model
#' @param t Implicit argument for time
#' @param logx A vector with values for the log-states
#' @param parms A vector with parameter values for the dynamical system
#' @return A list of gradients for the log system
#' @examples
#' require(deSolve)
#' times = seq(0, 50, by=1/520)
#' paras = c(gamma = 0.0397, b = 0.836, a = 1.34, sigma = 7.5,
#' alpha = 66.36, beta = 33.25, c = 0, rho = 0.8)
#' start = log(c(X=12.69/2, H1=0.1, H2=0.1, Y = 0.1, I = 0.1))
#' out = as.data.frame(ode(start, times, coyne, paras))
#' @export
coyne=function(t, logx, parms){
x=exp(logx)
X=x[1]
H1=x[2]
H2=x[3]
Y=x[4]
I=x[5]
N = sum(x)
with(as.list(parms),{
dX = a * (X + I) - beta * X * Y - gamma * N * X - (b + c) * X
dH1= rho * beta * X * Y - gamma * N * H1 - (b + sigma + c) * H1
dH2= (1-rho) * beta * X * Y - gamma * N * H2 - (b + sigma + c) * H2
dY = sigma * H1 - gamma * N * Y - (b + alpha + c) * Y
dI = sigma * H2 - gamma * N * I - (b + c) * I
res=c(dX/X, dH1/H1, dH2/H2, dY/Y, dI/I)
list(res)
})
}
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