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#' Fitting a simple viral infection models to influenza data
#'
#' @description This function runs a simulation of a compartment model
#' using a set of ordinary differential equations.
#' The model describes a simple viral infection system.
#' @param U : initial number of uninfected target cells : numeric
#' @param I : initial number of infected target cells : numeric
#' @param V : initial number of infectious virions : numeric
#' @param n : rate of uninfected cell production : numeric
#' @param dU : rate at which uninfected cells die : numeric
#' @param dI : rate at which infected cells die : numeric
#' @param g : unit conversion factor : numeric
#' @param p : rate at which infected cells produce virus : numeric
#' @param plow : lower bound for p : numeric
#' @param phigh : upper bound for p : numeric
#' @param psim : rate at which infected cells produce virus for simulated data : numeric
#' @param b : rate at which virus infects cells : numeric
#' @param blow : lower bound for infection rate : numeric
#' @param bhigh : upper bound for infection rate : numeric
#' @param bsim : rate at which virus infects cells for simulated data : numeric
#' @param dV : rate at which infectious virus is cleared : numeric
#' @param dVlow : lower bound for virus clearance rate : numeric
#' @param dVhigh : upper bound for virus clearance rate : numeric
#' @param dVsim : rate at which infectious virus is cleared for simulated data : numeric
#' @param noise : noise to be added to simulated data : numeric
#' @param iter : max number of steps to be taken by optimizer : numeric
#' @param solvertype : the type of solver/optimizer to use (1-3) : numeric
#' @param usesimdata : set to 1 if simulated data should be fitted, 0 otherwise : numeric
#' @return The function returns a list containing as elements the best fit time series data frame, the best fit parameters,
#' the data and the final SSR
#' @details A simple compartmental ODE model mimicking acute viral infection
#' is fitted to data.
#' Data can either be real or created by running the model with known parameters and using the simulated data to
#' determine if the model parameters can be identified.
#' The fitting is done using solvers/optimizers from the nloptr package (which is a wrapper for the nlopt library).
#' The package provides access to a large number of solvers.
#' Here, we only implement 3 solvers, namely 1 = NLOPT_LN_COBYLA, 2 = NLOPT_LN_NELDERMEAD, 3 = NLOPT_LN_SBPLX
#' For details on what those optimizers are and how they work, see the nlopt/nloptr documentation.
#' @section Warning: This function does not perform any error checking. So if
#' you try to do something nonsensical (e.g. specify negative parameter or starting values,
#' the code will likely abort with an error message.
#' @examples
#' # To run the code with default parameters just call the function:
#' \dontrun{result <- simulate_basicvirus_fit()}
#' # To apply different settings, provide them to the simulator function, like such:
#' result <- simulate_basicvirus_fit(iter = 5)
#' @seealso See the Shiny app documentation corresponding to this
#' function for more details on this model.
#' @author Andreas Handel
#' @importFrom utils read.csv
#' @importFrom dplyr filter rename select
#' @importFrom nloptr nloptr
#' @export
simulate_basicvirus_fit <- function(U = 1e6, I = 0, V = 1,
n = 0, dU = 0, dI = 2, g = 0,
p = 1e-3, plow = 1e-4, phigh = 1e2, psim = 1e-3,
b = 1e-1, blow = 1e-3, bhigh = 1e1, bsim = 1e-1,
dV = 1, dVlow = 1e-2, dVhigh = 1e2, dVsim = 1,
noise = 0, iter = 1, solvertype = 1, usesimdata = 0)
{
###################################################################
#function that fits the ODE model to data
###################################################################
basicfitfunction <- function(params, fitdata, Y0, xvals, fixedpars, fitparnames, LOD)
{
names(params) = fitparnames #for some reason nloptr strips names from parameters
allpars = c(Y0,params, tfinal = max(xvals), dt = 0.1, tstart = 0, fixedpars)
#this function catches errors
odeout <- try(do.call(DSAIRM::simulate_basicvirus_ode, as.list(allpars)));
#extract values for virus load at time points where data is available
modelpred = odeout$ts[match(fitdata$xvals,odeout$ts[,"time"]),"V"];
#since the ODE returns values on the original scale, we need to transform it into log10 units for the fitting procedure
#due to numerical issues in the ODE model, virus might become negative, leading to problems when log-transforming.
#Therefore, we enforce a minimum value of 1e-10 for virus load before log-transforming
logvirus=c(log10(pmax(1e-10,modelpred)));
#since the data is censored,
#set model prediction to LOD if it is below LOD
#this means we do not penalize model predictions below LOD
logvirus[(fitdata$outcome<=LOD & (fitdata$outcome-logvirus)>0)] = LOD
#return the objective function, the sum of squares,
#which is being minimized by the optimizer
return(sum((logvirus-fitdata$outcome)^2))
} #end function that fits the ODE model to the data
#will contain final result
result <- list()
#some settings for ode solver and optimizer
#those are hardcoded here, could in principle be rewritten to allow user to pass it into function
atolv=1e-8; rtolv=1e-8; #accuracy settings for the ODE solver routine
maxsteps = iter #number of steps/iterations for algorithm
#load data
#This data is from Hayden et al 1996 JAMA
#We only use the data for the no-drug condition here
LOD = hayden96flu$LOD[1] #limit of detection, log scale
fitdata = subset(hayden96flu, txtime == 200, select=c("HoursPI", "LogVirusLoad")) #only fit some of the data
colnames(fitdata) = c("xvals",'outcome')
#convert to days
fitdata$xvals = fitdata$xvals / 24
Y0 = c(U = U, I = I, V = V); #combine initial conditions into a vector
xvals = seq(0, max(fitdata$xvals), 0.1); #vector of times for which solution is returned (not that internal timestep of the integrator is different)
#if we want to fit simulated data
if (usesimdata == 1)
{
#combining fixed parameters and to be estimated parameters into a vector
modelpars = c(n=n,dU=dU,dI=dI,dV=dVsim,b = bsim,p=psim,g=g);
allpars = c(Y0,tfinal = max(fitdata$xvals), tstart = 0, dt = 0.1, modelpars)
#simulate model with known parameters to get artifitial data
#not sure why R needs it in such a weird form
#but supplying vector of values to function directly doesn't work
odeout <- do.call(DSAIRM::simulate_basicvirus_ode, as.list(allpars))
simres = odeout$ts
#extract values for virus load at time points where data is available
simdata = data.frame(simres[match(fitdata$xvals,simres[,"time"]),])
simdata$simres = log10(simdata$V)
simdata = subset(simdata, select=c('time', 'simres'))
colnames(simdata) = c('xvals','outcome')
fitdata$outcome = simdata$outcome + noise*stats::runif(length(simdata$outcome),-1,1)*simdata$outcome
}
#combining fixed parameters and to be estimated parameters into a vector
fixedpars = c(n=n,dU=dU,dI=dI,g=g)
par_ini = as.numeric(c(p, b, dV))
lb = as.numeric(c(plow, blow, dVlow))
ub = as.numeric(c(phigh, bhigh, dVhigh))
fitparnames = c('p', 'b', 'dV')
if (solvertype == 1) {algname = "NLOPT_LN_COBYLA"}
if (solvertype == 2) {algname = "NLOPT_LN_NELDERMEAD"}
if (solvertype == 3) {algname = "NLOPT_LN_SBPLX"}
#this line runs the simulation, i.e. integrates the differential equations describing the infection process
#the result is saved in the odeoutput matrix, with the 1st column the time, all other column the model variables
#in the order they are passed into Y0 (which needs to agree with the order in virusode)
bestfit = nloptr::nloptr(x0=par_ini, eval_f=basicfitfunction,lb=lb,ub=ub,opts=list("algorithm"=algname,xtol_rel=1e-10,maxeval=maxsteps,print_level=0), fitdata=fitdata, Y0 = Y0, xvals = xvals, fixedpars=fixedpars,fitparnames=fitparnames,LOD=LOD)
#extract best fit parameter values and from the result returned by the optimizer
params = bestfit$solution
names(params) = fitparnames #for some reason nloptr strips names from parameters
modelpars = c(params,fixedpars)
allpars = c(Y0,modelpars,tfinal = max(fitdata$xvals))
#doe one final run of the ODE to get a time-series to report back
odeout <- do.call(simulate_basicvirus_ode, as.list(allpars))
simres = odeout$ts
#extract values for virus load at time points where data is available
modelpred = simres[match(fitdata$xvals,simres[,"time"]),"V"];
#compute SSR for final fit. See comments inside of fitting function for explanations.
modelpred = odeout$ts[match(fitdata$xvals,odeout$ts[,"time"]),"V"];
logvirus=c(log10(pmax(1e-10,modelpred)));
logvirus[(fitdata$outcome<=LOD & (fitdata$outcome-logvirus)>0)] = LOD
ssrfinal=(sum((logvirus-fitdata$outcome)^2))
#list structure that contains all output
result$ts = odeout$ts
result$bestpars = params
result$SSR = ssrfinal
#return the data not on a log scale for consistency
fitdata$outcome = 10^fitdata$outcome
fitdata$varnames = 'V_data'
colnames(fitdata) = c("xvals",'yvals','varnames')
result$data = fitdata
#The output produced by the fitting routine
return(result)
}
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