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Copy pathHEV metrop-hastings code for model5.R
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HEV metrop-hastings code for model5.R
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# HEV metrop-hastings code for model5.R
#( SEIIR model with moderately informative priors allowing transmisison rate to very depending on whether in the first or second I compartment)
# Ben Cooper 2016
# Fit the model to all three camps together using Metropolis-Hastings Algorithm
# estimating common natural history parameters and the proportion symptomaticc
# Model 5 does this with an SEIIR model with two levels of transmissibility (early and latet infectious)
#(by default with same parameters for leaving I1 and I2 so infectious period has erlang distribution)
#camp specific R0s, camp-specific time of first case but estimating
# gamma and proportion sympomatic which are the same for all three camps.
# Assume data follow Negative binomial distribution around predicted means
# and use compiled C code to run the ODE model (much faster)
# ************************************************************************************************
library(deSolve)
# first compiled and load the C code for the SEIR model
system("R CMD SHLIB SEEIR.c")
dyn.load("SEEIR.so")
system("R CMD SHLIB SEIIR.c")
dyn.load("SEIIR.so")
system("R CMD SHLIB SEIRforced.c")
dyn.load("SEIRforced.so")
Uganda<-read.csv("UgandaHepECases.csv")
Uganda[is.na(Uganda)]<-0
logit<-function(y){log(y/(1-y))}
inv.logit<-function(x){(exp(x)/(1+exp(x)))}
HepEmod.nowatsan <- function(t, x, parms) {
#modified version of model to allow transmission to vary according to Watsan interventions
# function returning a list holding the model equations and the rates of import and export of people into the opulation at diferent time points.
# Assumes a fixed population size and no vaccination
# t is time
#x is the vector of state variables (S, E, I, R)
# parms is the vector of parameters
with(as.list(c(parms, x)), {
# beta.max is max transmission parameter (when no water)
# beta.min is min seasonal transmission paramter (when unlimited water)
# r.water is the rate term in the model relating watsan intervention effects on water to beta
# r.latrines is the rate term in the model relating watsan intervention effects on latrines to beta
# phi is phase angle which determines what time of year peak(s) occurs
# N is current population size
# gamma is rate of progression to exposed to infectious
# rho is rate of progression from infectious to recovered.
N<-S+E+I+R
# beta<-seasonal.transmission.parameter(beta.max,beta.min,phi,t)
# w<-getwaterperp(t)
# #l<-getlatrinesperp(t)
# beta<-get.transmisison.parameter.given.watsan(beta.max,beta.min,r.water,w,r.latrines,l)
# Derivatives
beta<-beta.max
dS <- -beta*S*I/N
dE <- beta*S*I/N - gamma*E
dI <- gamma*E - rho*I
dR <- rho*I
dCumInc<-gamma*E
# Return values
list(c(dS,dE,dI,dR,dCumInc))
}) # end with
} # end HepEmod
getLLHepEmod.mh.combined.no.watsan<-function(params, x1,x2,x3, plot=FALSE,verbose=FALSE, SEEIR=FALSE, SEIIR=TRUE){
#The version is designed for use with Metropolis Hastings algorithm
# assumes no effect of watsan
# x1, x2, x3 are vectors of state variables (S, E, I, R) for each camp at start time (assume this vector is known )
# if SEEIR ==TRUE thihs uses the dll for the SEEIR model which assumes two equal comparments (by default with same rate of leaving
# so latent period has an erlang distribution)
# if SEIIR ==TRUE thihs uses the dll for the SEEIR model which assumes two equal comparments (by default with same rate of leaving
# so latent period has an erlang distribution)
with(as.list(c(params, x1,x2,x3)), {
# R01 is R0 in camp 1
# R02 is R0 in camp 2
# R03 is R0 in camp 3
# time.first.infected1 is time of first case in year 1 in camp 1 (scale is years)
# time.first.infected2 is time of first case in year 1 in camp 2 (scale is years)
# time.first.infected3 is time of first case in year 1 in camp 3 (scale is years)
# gamma is rate of progression to exposed to infectious
# rho is rate of progression from infectious to recovered (log(1/infectious period).
# proportion.symptomatic is proporotion of cases seen which are symptomatic
# proportion.of.transmission.early.in.infection - is proportion of total transmission due to the first I compartment
# weeks.from.infection.symptoms - delay till symptoms show (assumed constant)
# disp is the dispersion parameter for negative binomial likelihood. If NA use a Poisson likelihood
wk.first.infected1<-round(time.first.infected1*52)
wk.first.infected2<-round(time.first.infected2*52)
wk.first.infected3<-round(time.first.infected3*52)
wk<-1/52
# output first time point then regular weekly timesteps
times1<- seq(ceiling(time.first.infected1*52)/52, 157/52, by = wk)
times2<- seq(ceiling(time.first.infected2*52)/52, 157/52, by = wk)
times3<- seq(ceiling(time.first.infected3*52)/52, 157/52, by = wk)
if(time.first.infected1!=times1[1]) times1<-c(time.first.infected1,times1)
if(time.first.infected2!=times2[1]) times2<-c(time.first.infected2,times2)
if(time.first.infected3!=times3[1]) times3<-c(time.first.infected3,times3)
parameters1<-c(
beta=R01 *rho,
gamma=gamma,
rho=rho)
parameters2<-c(
beta=R02 *rho,
gamma=gamma,
rho=rho)
parameters3<-c(
beta=R03 *rho,
gamma=gamma,
rho=rho)
if(SEEIR==FALSE & SEIIR==FALSE){
out1<-ode(y=x1,times=times1, func="derivs",parms=parameters1,jacfun="jac",dllname="SEIR", initfunc="initmod",nout=1,outnames="Sum")
out2<-ode(y=x2,times=times2, func="derivs",parms=parameters2,jacfun="jac",dllname="SEIR", initfunc="initmod",nout=1,outnames="Sum")
out3<-ode(y=x3,times=times3, func="derivs",parms=parameters3,jacfun="jac",dllname="SEIR", initfunc="initmod",nout=1,outnames="Sum",maxsteps=1000000)
} else if(SEEIR==TRUE & SEIIR==FALSE) {
parameters1<-c(
beta=R01 *rho,
gamma1=gamma,
gamma2=gamma,
rho=rho)
parameters2<-c(
beta=R02 *rho,
gamma1=gamma,
gamma2=gamma,
rho=rho)
parameters3<-c(
beta=R03 *rho,
gamma1=gamma,
gamma2=gamma,
rho=rho)
out1<-ode(y=x1,times=times1, func="derivs",parms=parameters1,jacfun="jac",dllname="SEEIR", initfunc="initmod",nout=1,outnames="Sum",maxsteps=1000000)
out2<-ode(y=x2,times=times2, func="derivs",parms=parameters2,jacfun="jac",dllname="SEEIR", initfunc="initmod",nout=1,outnames="Sum",maxsteps=1000000)
out3<-ode(y=x3,times=times3, func="derivs",parms=parameters3,jacfun="jac",dllname="SEEIR", initfunc="initmod",nout=1,outnames="Sum",maxsteps=1000000)
} else if(SEEIR==FALSE & SEIIR==TRUE) { # in this case set parameter for model where beta1 =beta2 and rho1 = rho2
parameters1<-c(
beta1=proportion.of.transmission.early.in.infection*R01 *rho,
beta2=(1-proportion.of.transmission.early.in.infection)*R01 *rho,
gamma=gamma,
rho1=rho,
rho2=rho)
parameters2<-c(
beta1=proportion.of.transmission.early.in.infection*R02 *rho,
beta2=(1-proportion.of.transmission.early.in.infection)*R02 *rho,
gamma=gamma,
rho1=rho,
rho2=rho)
parameters3<-c(
beta1=proportion.of.transmission.early.in.infection*R03 *rho,
beta2=(1-proportion.of.transmission.early.in.infection)*R03 *rho,
gamma=gamma,
rho1=rho,
rho2=rho)
out1<-ode(y=x1,times=times1, func="derivs",parms=parameters1,jacfun="jac",dllname="SEIIR", initfunc="initmod",nout=1,outnames="Sum",maxsteps=1000000)
out2<-ode(y=x2,times=times2, func="derivs",parms=parameters2,jacfun="jac",dllname="SEIIR", initfunc="initmod",nout=1,outnames="Sum",maxsteps=1000000)
out3<-ode(y=x3,times=times3, func="derivs",parms=parameters3,jacfun="jac",dllname="SEIIR", initfunc="initmod",nout=1,outnames="Sum",maxsteps=1000000)
} else {
stop("Something has gone wrong. This should not happen.")
}
cuminc1<-out1[,6][-1] # the [-1] drops the first time point for cuminc, so we start counting at exact times of each new week
cuminc2<-out2[,6][-1]
cuminc3<-out3[,6][-1]
n1<-length(cuminc1)
n2<-length(cuminc2)
n3<-length(cuminc3)
weeklyinc1<-c(cuminc1[1],cuminc1[2:n1]-cuminc1[1:(n1-1)]) # weekly incidence
weeklyinc2<-c(cuminc2[1],cuminc2[2:n2]-cuminc2[1:(n2-1)]) # weekly incidence
weeklyinc3<-c(cuminc3[1],cuminc3[2:n3]-cuminc3[1:(n3-1)]) # weekly incidence
# now use weeklyinc to construct a likelihood
# Could use a binomial likelihood noting that dbinom returns a 0 if number of trials is fewer than
# number successes (so returned log likelihood will be -Inf)
# below OBSERVED.CASES is the actual data (specified as global variable)
# and the likelihood is calculated starting at LATEST.START.WEEK (last time virus could be introduced into camp)
# However using a poisson or negbin likelihood is more robust (and negbin is likely to fit much better)
obs1<-OBSERVED.CASES1[(LATEST.START.WEEK1+1):length(OBSERVED.CASES1)] # only use obs after LATEST.START.WEEK in LL
obs2<-OBSERVED.CASES2[(LATEST.START.WEEK2+1):length(OBSERVED.CASES2)] # only use obs after LATEST.START.WEEK in LL
obs3<-OBSERVED.CASES3[(LATEST.START.WEEK3+1):length(OBSERVED.CASES3)] # only use obs after LATEST.START.WEEK in LL
wk.inc1<-weeklyinc1[1:(n1-weeks.from.infection.symptoms)] # this gives total incident infectious caes - a proportion of whcih will be symptomatic & reported after a delay of weeks.from.infection.symptoms
wk.inc2<-weeklyinc2[1:(n2-weeks.from.infection.symptoms)]
wk.inc3<-weeklyinc3[1:(n3-weeks.from.infection.symptoms)]
# now discard values of incidence before the first obs we consider in the likelihood
numbertochop1<-length(wk.inc1)-length(obs1)
numbertochop2<-length(wk.inc2)-length(obs2)
numbertochop3<-length(wk.inc3)-length(obs3)
wk.inc1<-wk.inc1[(numbertochop1+1):length(wk.inc1)]
wk.inc2<-wk.inc2[(numbertochop2+1):length(wk.inc2)]
wk.inc3<-wk.inc3[(numbertochop3+1):length(wk.inc3)]
if(verbose){
print(c(numbertochop1,numbertochop2,numbertochop3))
print(obs1/wk.inc1) # should be less than one for a feasible value
print(obs2/wk.inc2)
print(obs3/wk.inc3)
}
#binomLL<- sum(dbinomLLterms1) +sum(dbinomLLterms2) +sum(dbinomLLterms3)
disp<-params$disp
if(is.na(disp)){ # then use Poisson likelihood
LLterms1<-dpois(obs1, wk.inc1 * proportion.symptomatic,log=TRUE)
LLterms2<-dpois(obs2, wk.inc2 * proportion.symptomatic,log=TRUE)
LLterms3<-dpois(obs3, wk.inc3 * proportion.symptomatic,log=TRUE)
} else { # then use negbin likelihood
LLterms1<-dnbinom(obs1,mu= wk.inc1 * proportion.symptomatic,size=disp, log=TRUE)
LLterms2<-dnbinom(obs2,mu= wk.inc2 * proportion.symptomatic,size=disp,log=TRUE)
LLterms3<-dnbinom(obs3,mu= wk.inc3 * proportion.symptomatic,size=disp,log=TRUE)
}
# print(proportion.symptomatic)
# print(round(wk.inc1))
# print(round(wk.inc2))
# print(round(wk.inc3))
# print(dPoisLLterms1)
# print(dPoisLLterms2)
# print(dPoisLLterms3)
LL<-sum(LLterms1)+sum(LLterms2)+sum(LLterms3)
if(plot==TRUE){
expected.cases1<-proportion.symptomatic*wk.inc1
expected.cases2<-proportion.symptomatic*wk.inc2
expected.cases3<-proportion.symptomatic*wk.inc3
ymax=max(obs1,obs2,obs3,expected.cases1,expected.cases2,expected.cases3)
plot(obs1,type='p',col="red",ylim=c(0,ymax))
lines(expected.cases1,type='l',col="red")
points(obs2,col="blue",ylim=c(0,ymax))
lines(expected.cases2,type='l',col="blue")
points(obs3,col="green",ylim=c(0,ymax))
lines(expected.cases3,type='l',col="green")
}
# n.trials=sum(wk.inc1)+sum(wk.inc2)+sum(wk.inc3) # number of binomial trials (needed for Gibss updates)
#n.successes=sum(obs1)+sum(obs2)+sum(obs3)
# return(list(LL=binomLL,n.trials=n.trials,n.successes=n.successes))
return(list(LL=LL))
})
}
LATEST.START.WEEK1<-50 # last week in year one when epidemic could start. (use 50 for camp1, 43 for camp 2 and 47 for camp 3) to allow for delay to first cas
LATEST.START.WEEK2<-43
LATEST.START.WEEK3<-47
#LATEST.START.WEEK3<-49
# should be weeks.from.infection.symptoms before first case is seen
OBSERVED.CASES1<-Uganda[,2]
OBSERVED.CASES2<-Uganda[,3]
OBSERVED.CASES3<-Uganda[,4]
watsantimes<-c(71/52,87/52,81/52) # times of watsan intervention start in time units of year (see UgandaWaterPerPerson.csv)
#fixed
Uganda.wpp<-read.csv("UgandaWaterPerPerson.csv")
Uganda.san<-read.csv("Uganda_Latrines.csv")
N1<-16689 # Population size of Agoro
N2<-10442 # Population size of MadiOpei
N3<-10555 # Population size of Paloga
wks.to.symptoms<-1 # i.e. delay in weeks from onset of infectiousness to onset of symptoms
# initial values
init.latent.period<-2/52 # in units of 1 year (values between 2 and 7 weeks are plausible apparently)
init.infectious.period<-2/52 # values of about 2 weeks are plausible
init.propSymptoms<-1/7 # Assumed value for proportion symptomatic
init.R0<-4
E0<-1
I0<-0
R0<-0
CumInc0<-0
xstart1<-c(S=N1-1,E=E0,I=I0, R=R0, CumInc=CumInc0)
xstart2<-c(S=N2-1,E=E0,I=I0, R=R0, CumInc=CumInc0)
xstart3<-c(S=N3-1,E=E0,I=I0, R=R0, CumInc=CumInc0)
###### Metropolis-Hastings sampling
# we want to make inference about the following parameters:
# R01, R02, R03 - the basic reproduction numbers in each of the three camps
# gamma - rate of progression from latently infected to infectious (1/latent.period)
# rho - rate of recovery for those who are infectious (1/infectious.period)
# propSymptoms - proportion of people who have symptoms
# time.firstcase1 time.firstcase2 time.firstcase3 - time of first case in each of the three camps
# 1. Define Prior distributions
# we give R0 priors on [1,10]
# we give gamma a diffuse gamma prior
# we give rho a diffuse gamma prior
# time.firstcase1 priors on [1,LATEST.START.WEEK1/52] (time in units of years)
# we give propSymptoms a flat beta prior beta(1,1) which takes values between 0 and 1
#
# # Uninformative priors below
R0.prior.density<-function(x){ dunif(x, min=1, max=20)} #note we can either parameterise for R0 or for beta, but not both...
#beta.prior.density<-function(x){ dgamma(x, shape=0.001,rate=0.001)} #as R0=beta/rho
beta.prior.density<-function(x){ dunif(x, 0.0001,500)} #as
gamma.prior.density<-function(x){ dgamma(x, shape=0.001,rate=0.001)}
rho.prior.density<-function(x){ dgamma(x, shape=0.001,rate=0.001)}
time.first.infected1.prior.density<-function(x){ dunif(x, min=0, max=LATEST.START.WEEK1/52)}
time.first.infected2.prior.density<-function(x){ dunif(x, min=0, max=LATEST.START.WEEK2/52)}
time.first.infected3.prior.density<-function(x){ dunif(x, min=0, max=LATEST.START.WEEK3/52)}
propSymptoms.prior.beta.shape1<-1 # parmeters for propSymptoms.prior
propSymptoms.prior.beta.shape2<-1 # parmeters for propSymptoms.prior
propSymptoms.prior.density<-function(x){ dbeta(x, propSymptoms.prior.beta.shape1,propSymptoms.prior.beta.shape2)}
proportion.of.transmission.early.in.infection.density<-function(x){ dbeta(x, 1,1)}
disp.prior.density<-function(x){ dunif(x, min=0.1, max=10000)}
# Informative priors below
#
R0.prior.density<-function(x){ dunif(x, min=1, max=30)} #note we can either parameterise for R0 or for beta, but not both...
# beta.prior.density<-function(x){ dgamma(x, shape=0.001,rate=0.001)} #as R0=beta/rho
beta.prior.density<-function(x){ dunif(x, 0.0001,500)} #as
gamma.prior.density<-function(x){ dgamma(x, shape=1,rate=0.0932)} #rate is 34/365. Conjugate based on one observation with a mean latent period of 34 days
# rho.prior.density<-function(x){ dgamma(x, shape=11,rate=1.145)}
rho.prior.density<-function(x){ dgamma(x, shape=22,rate=1.145)} #SEIIR - twice rate in each I, so half duration .
# #above based on Takahashi et al 2007: 11 patients with a mean duration of infectiousness of 38 days (assuming 1 week infectious before symptoms)
# #conjugate gamma shape and rate are shape=a+n,rate=r +n*x if prior has shape a and rate r
# #and if n observation with a mean of x. Time units are in years here
# time.first.infected1.prior.density<-function(x){ dunif(x, min=0, max=LATEST.START.WEEK1/52)}
# time.first.infected2.prior.density<-function(x){ dunif(x, min=0, max=LATEST.START.WEEK2/52)}
# time.first.infected3.prior.density<-function(x){ dunif(x, min=0, max=LATEST.START.WEEK3/52)}
# propSymptoms.prior.beta.shape1<-2 # parmeters for propSymptoms.prior (corresponds to week evidence that 1 in 8 positive)
# propSymptoms.prior.beta.shape2<-8 # parmeters for propSymptoms.prior
# propSymptoms.prior.density<-function(x){ dbeta(x, propSymptoms.prior.beta.shape1,propSymptoms.prior.beta.shape2)}
# disp.prior.density<-function(x){ dunif(x, min=0.1, max=10000)}
# watsan.effect.prior.density<-function(x){ dnorm(x, mean=0, sd=100)}
# 2. Define functions to propose new values for parameters
# Adjust variance of the proposals to tune the algorithm (ideally we want to accept about a fifth of proposals for each variable)
# Note that these functions may propose values outside possible ranges, but since prior distributions
# will have zero probability at these values they have no chance of being accepted
generate.proposal.R0<-function(currentR0){return(currentR0 + rnorm(1,0,.1))}
generate.proposal.beta<-function(currentbeta){return(currentbeta + rnorm(1,0,5))}
generate.proposal.gamma<-function(currentgamma){return(currentgamma + rnorm(1,0,.4))}
generate.proposal.rho<-function(currentrho){return(currentrho + rnorm(1,0,.4))}
generate.proposal.time.first.infected<-function(currenttime){return(currenttime + rnorm(1,0,.01))}
generate.proposal.propSymptoms<-function(currentprop){return(currentprop + rnorm(1,0,.01))} # used if using Poisson likelihood (if binom likilihood use a Gibbs update for this one)
generate.proposal.proportion.of.transmission.early.in.infection <-function(currentprop){return(currentprop + rnorm(1,0,.01))} # only for SEIIR model
generate.proposal.disp<-function(currentdisp){return(currentdisp + rnorm(1,0,2))}
generate.proposal.watsan.effect<-function(currentw){return(currentw + rnorm(1,0,50))}
# initial values
parameters<-list(
R01=4,
R02=5,
R03=6,
gamma=10.4,
rho=20,
proportion.of.transmission.early.in.infection=0.5, #only relevant in SEIIR model
time.first.infected1=0.87,
time.first.infected2=0.7,
time.first.infected3=0.83,
proportion.symptomatic=init.propSymptoms,
weeks.from.infection.symptoms=1,
disp=1 # dispersion for negative binomial likelihood. Set to NA to use a Poisson likelihood
# w1=0, #watsan effect in camp1 - comment out if not using watsan model
# w2=0, #watsan effect in camp2 - comment out if not using watsan model
#w3=0# watsan effect in camp3 - comment out if not using watsan model
)
# parameters$disp<-NA # setting to NA forces a Poisson likelihood
parameters<-unlist(parameters)
parameters<-as.data.frame(t(parameters))
#thin<-10
# with version 1.8 we can do about 20000 runs in one hour - we need to do about 3 million runs in total so really a week long runs are needed.
thin<-100
N<-3000000
#last.posterior.samples<-posterior.samples
#parameters<-modv1.670to1670k.posterior.samples[10001,1:10]
m<-dim(last.posterior.samples)[1]
#parameters<-last.posterior.samples[m,1:11]
#parameters<-last.posterior.samples[m,]
#parameters$w1<-0
#parameters$w2<-0
#parameters$w3<-0
#parameters$time.first.infected3<-0.9
#parameters$disp<-5
# parameters<-posterior.samples.150k.negbin[m,1:11]
proposed.parameters<-parameters
#parameters$disp<-1
#current.loglikelihood<-getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3,Uganda.wpp, plot=TRUE)
#parameters$disp<-1
#current.loglikelihood<-getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3,Uganda.wpp, plot=TRUE)
# Below the SEIIR option, if set to tree, causes likelihood to be based on SEIIR model, where time is in two
# I compartments is equal (giving an erlang distributed infectious period - though if using this should use different priors
# for the rho parameters )
current.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE, SEIIR=TRUE)
#store results from the posterior sample with one column for each parameter & one for LL
posterior.samples<-as.data.frame(matrix(c(as.numeric(parameters),current.loglikelihood$LL),nrow=1))
colnames(posterior.samples)<-c(names(as.vector(parameters)),"LL")
beta1moves.accepted<-0 # note that we either update R0s or betas but not both
beta2moves.accepted<-0 # note that we either update R0s or betas but not both
beta3moves.accepted<-0 # note that we either update R0s or betas but not both
R01moves.accepted<-0 # note that we either update R0s or betas but not both
R02moves.accepted<-0 # note that we either update R0s or betas but not both
R03moves.accepted<-0 # note that we either update R0s or betas but not both
beta.moves.accepted<-0
gamma.moves.accepted<-0
rho.moves.accepted<-0
proportion.of.transmission.early.in.infection.moves.accepted<-0
time.infected1.moves.accepted<-0
time.infected2.moves.accepted<-0
time.infected3.moves.accepted<-0
propSymptoms.moves.accepted<-0
disp.moves.accepted<-0
w1.moves.accepted<-0
w2.moves.accepted<-0
w3.moves.accepted<-0
for(i in 1:N){
# updates to beta1, beta1, and beta3 (not blocked together)
#proposed.parameters$R01<-generate.proposal.R0(parameters$R01) # proposed update
proposed.beta1<-generate.proposal.beta(parameters$R01*parameters$rho) # proposed update
proposed.parameters$R01<-proposed.beta1/parameters$rho
#current.prior.density<-R0.prior.density(parameters$R01)
current.prior.density<-beta.prior.density(parameters$R01*parameters$rho)
proposal.prior.density<-beta.prior.density(proposed.beta1)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
#print(c("R0 accept prob",acceptance.prob ))
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
beta1moves.accepted<-beta1moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else {
proposed.parameters<-parameters
}
#proposed.parameters$R02<-generate.proposal.R0(parameters$R02) # proposed update
proposed.beta2<-generate.proposal.beta(parameters$R02*parameters$rho) # proposed update
proposed.parameters$R02<-proposed.beta2/ parameters$rho
#current.prior.density<-R0.prior.density(parameters$R01)
current.prior.density<-beta.prior.density(parameters$R02*parameters$rho)
proposal.prior.density<-beta.prior.density(proposed.beta2)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
#print(c("R0 accept prob",acceptance.prob ))
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
beta2moves.accepted<-beta2moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else {
proposed.parameters<-parameters
}
proposed.beta3<-generate.proposal.beta(parameters$R03*parameters$rho) # proposed update
proposed.parameters$R03<-proposed.beta3/ parameters$rho
#current.prior.density<-R0.prior.density(parameters$R01)
current.prior.density<-beta.prior.density(parameters$R03*parameters$rho)
proposal.prior.density<-beta.prior.density(proposed.beta3)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
#print(c("R0 accept prob",acceptance.prob ))
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
beta3moves.accepted<-beta3moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else {
proposed.parameters<-parameters
}
# updates to gamma
proposed.parameters$gamma<-generate.proposal.gamma(parameters$gamma) # proposed update
current.prior.density<-gamma.prior.density(parameters$gamma)
proposal.prior.density<-gamma.prior.density(proposed.parameters$gamma)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
gamma.moves.accepted<-gamma.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
# updates to rho
proposed.parameters$rho<-generate.proposal.rho(parameters$rho) # proposed update
proposed.parameters$R01<-parameters$R01*parameters$rho/ proposed.parameters$rho
proposed.parameters$R02<-parameters$R02*parameters$rho/ proposed.parameters$rho
proposed.parameters$R03<-parameters$R03*parameters$rho/ proposed.parameters$rho
current.prior.density<-rho.prior.density(parameters$rho)
proposal.prior.density<-rho.prior.density(proposed.parameters$rho)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
rho.moves.accepted<-rho.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
# updates to time.first.infected1, time.first.infected2, and time.first.infected3 (no longer blocked together)
proposed.parameters$time.first.infected1<-generate.proposal.time.first.infected(parameters$time.first.infected1) # proposed update
current.prior.density<-time.first.infected1.prior.density(parameters$time.first.infected1)
proposal.prior.density<-time.first.infected1.prior.density(proposed.parameters$time.first.infected1)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
time.infected1.moves.accepted<-time.infected1.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
proposed.parameters$time.first.infected2<-generate.proposal.time.first.infected(parameters$time.first.infected2) # proposed update
current.prior.density<-time.first.infected2.prior.density(parameters$time.first.infected2)
proposal.prior.density<-time.first.infected2.prior.density(proposed.parameters$time.first.infected2)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
time.infected2.moves.accepted<-time.infected2.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
proposed.parameters$time.first.infected3<-generate.proposal.time.first.infected(parameters$time.first.infected3) # proposed update
current.prior.density<-time.first.infected3.prior.density(parameters$time.first.infected3)
proposal.prior.density<-time.first.infected3.prior.density(proposed.parameters$time.first.infected3)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
time.infected3.moves.accepted<-time.infected3.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
# updates to proportion.symptomatic
# (this can be done with a Gibbs step, as we have a beta prior and binomial likelihood (and don't change number of trials))
# If the prior for the probability of success (in this case reporting of a case) is beta(a, b),
# and we have n trials with x successes, then the posterior for the probability of success will
# be beta(a+x, b+n-x). We can use this fact to use a Gibbs step in updating
proposed.parameters$proportion.symptomatic<-generate.proposal.propSymptoms(parameters$proportion.symptomatic) # proposed update
current.prior.density<-propSymptoms.prior.density(parameters$proportion.symptomatic)
proposal.prior.density<-propSymptoms.prior.density(proposed.parameters$proportion.symptomatic)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
propSymptoms.moves.accepted<-propSymptoms.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
# updates to proportion.of.transmission.early.in.infection
proposed.parameters$proportion.of.transmission.early.in.infection <-generate.proposal.proportion.of.transmission.early.in.infection(parameters$proportion.of.transmission.early.in.infection) # proposed update
current.prior.density<- proportion.of.transmission.early.in.infection.density(parameters$proportion.of.transmission.early.in.infection)
proposal.prior.density<-proportion.of.transmission.early.in.infection.density(proposed.parameters$proportion.of.transmission.early.in.infection)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
proportion.of.transmission.early.in.infection.moves.accepted<-proportion.of.transmission.early.in.infection.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
# updates to disp (dispersion parameter for negative binomial likeihood [if it is NA use Poisson likelihood insted])
if(!is.na(parameters$disp)){
proposed.parameters$disp<-generate.proposal.disp(parameters$disp) # proposed update
current.prior.density<-disp.prior.density(parameters$disp)
proposal.prior.density<-disp.prior.density(proposed.parameters$disp)
if(proposal.prior.density>0) { # no point running the model if proposal is outside feasbile range as acceptance.prob will be zero
proposal.loglikelihood<-getLLHepEmod.mh.combined.no.watsan(proposed.parameters, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)
acceptance.prob<-min(1, exp(proposal.loglikelihood$LL- current.loglikelihood$LL)* proposal.prior.density/current.prior.density)
if(runif(1)<acceptance.prob){
parameters <- proposed.parameters
current.loglikelihood<- proposal.loglikelihood
disp.moves.accepted<-disp.moves.accepted+1
} else proposed.parameters<-parameters # otherwise current parameters stay the same
} else proposed.parameters<-parameters
}
# now store results of this iteration if i is a multiple of the parameter "thin"
if(i%% thin ==0) {
new.posterior.sample<-as.data.frame(matrix(c(as.numeric(parameters),current.loglikelihood$LL),nrow=1))
colnames(new.posterior.sample)<-c(names(as.vector(parameters)),"LL")
posterior.samples<-rbind(posterior.samples, new.posterior.sample)
print(c(i,c(as.numeric(parameters),current.loglikelihood$LL)))
}
} # end of main MCMC loops
# Summzarize accepteance probs
print(c("Accept ratio for beta1", beta1moves.accepted/N))
print(c("Accept ratio for beta2", beta2moves.accepted/N))
print(c("Accept ratio for beta3", beta3moves.accepted/N))
#print(c("Accept ratio for R01", R01moves.accepted/N))
#print(c("Accept ratio for R02", R02moves.accepted/N))
#print(c("Accept ratio for R03", R03moves.accepted/N))
print(c("Accept ratio for gamma", gamma.moves.accepted/N))
print(c("Accept ratio for rho", rho.moves.accepted/N))
print(c("Accept ratio for proportion.of.transmission.early.in.infection.moves.accepted", proportion.of.transmission.early.in.infection.moves.accepted/N))
print(c("Accept ratio for time.infected 1", time.infected1.moves.accepted/N))
print(c("Accept ratio for time.infected 2", time.infected2.moves.accepted/N))
print(c("Accept ratio for time.infected 3", time.infected3.moves.accepted/N))
print(c("Accept ratio for prop symptomatic 3", propSymptoms.moves.accepted/N))
print(c("Accept ratio for disp", disp.moves.accepted/N))
print(c("Accept ratio for w1", w1.moves.accepted/N))
print(c("Accept ratio for w2", w2.moves.accepted/N))
print(c("Accept ratio for w3", w3.moves.accepted/N))
#save.image()
save.image("model5 SEIIR different trans from I1 and I2 no watsan MH1.10 inf (uninfbeta) priors 3M thin 100.RData")
# plot selected runs
pdf("model5 SEIIR - selected fits from .3M (thin 100) chain.pdf")
par(mfrow=c(3,2),mar=c(4,4,1,1))
parameters<-posterior.samples[1,]
#getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3, Uganda.wpp, plot=TRUE)
getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE, SEIIR=TRUE)
#
parameters<-posterior.samples[3000,]
#getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3, Uganda.wpp, plot=TRUE)
getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE, SEIIR =TRUE)
parameters<-posterior.samples[6000,]
#getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3, Uganda.wpp, plot=TRUE)
getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE, SEIIR =TRUE)
parameters<-posterior.samples[9000,]
#getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3, Uganda.wpp, plot=TRUE)
getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE, SEIIR =TRUE)
parameters<-posterior.samples[12000,]
#getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3, Uganda.wpp, plot=TRUE)
getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE, SEIIR =TRUE)
parameters<-posterior.samples[15000,]
#getLLHepEmod.mh.combined.wpp.watsan(parameters, xstart1,xstart2,xstart3, Uganda.wpp, plot=TRUE)
getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE, SEIIR =TRUE)
#
#parameters<-posterior.samples[10000,]
#getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE)
#
#parameters<-posterior.samples[15000,]
#getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE)
#
#parameters<-posterior.samples[25000,]
#getLLHepEmod.mh.combined.no.watsan(parameters, xstart1,xstart2,xstart3, plot=TRUE)
#
dev.off()
#posterior.samples<-rbind(modv1.5_1.5mrunsthin100.NBLLflatpriors.posterior.samples[,1:11],posterior.samples[,1:11])
# plot chains
pdf("model5 SEIIR inf priors NBLL 3M runs thin 100.pdf")
par(mfrow=c(3,4),mar=c(4,4,1,1))
rows.to.plot<-seq(1,length(posterior.samples$R01),1)
plot(posterior.samples$R01[rows.to.plot],type='l',main="R01")
plot(posterior.samples$R02[rows.to.plot],type='l',main="R02")
plot(posterior.samples$R03[rows.to.plot],type='l',main="R03")
plot(posterior.samples$time.first.infected1[rows.to.plot],type='l',main="Time first infection 1")
plot(posterior.samples$time.first.infected2[rows.to.plot],type='l',main="Time first infection 2")
plot(posterior.samples$time.first.infected3[rows.to.plot],type='l',main="Time first infection 3")
plot(posterior.samples$gamma[rows.to.plot],type='l',main="gamma")
plot(posterior.samples$rho[rows.to.plot],type='l',main="rho")
plot(posterior.samples$proportion.symptomatic[rows.to.plot],type='l',main="Proportion symptomatic")
#plot(posterior.samples$w1[rows.to.plot],type='l',main="watsan camp 1")
#plot(posterior.samples$w2[rows.to.plot],type='l',main="watsan camp 2")
#plot(posterior.samples$w3[rows.to.plot],type='l',main="watsan camp 3")
dev.off()
# plot correlation
#pdf("model5 SEIIR inf prior NBLL 3M correlation.pdf")
par(mfrow=c(3,3),mar=c(4,4,1,1))
rows.to.plot<-seq(1,length(posterior.samples$R01),1)
plot(posterior.samples$R01[rows.to.plot],posterior.samples$gamma[rows.to.plot],xlab="R01",ylab="gamma",type='p',main="R01 v gamma",pch=".")
plot(posterior.samples$R01[rows.to.plot],posterior.samples$rho[rows.to.plot],xlab="R01",ylab="rho",type='p',main="R01 v rho",pch=".")
plot(posterior.samples$R01[rows.to.plot]*posterior.samples$rho[rows.to.plot],posterior.samples$rho[rows.to.plot],xlab="beta1",ylab="rho",type='p',main="beta1 v rho",pch=".")
plot(posterior.samples$R02[rows.to.plot]*posterior.samples$rho[rows.to.plot],posterior.samples$rho[rows.to.plot],xlab="beta2",ylab="rho",type='p',main="beta2 v rho",pch=".")
plot(posterior.samples$R03[rows.to.plot]*posterior.samples$rho[rows.to.plot],posterior.samples$rho[rows.to.plot],xlab="beta3",ylab="rho",type='p',main="beta3 v rho",pch=".")
plot(posterior.samples$R01[rows.to.plot],posterior.samples$time.first.infected1[rows.to.plot],xlab="R01",ylab="time.first.infected1",type='p',main="R01 v time.first.infected1",pch=".")
plot(posterior.samples$rho[rows.to.plot],posterior.samples$gamma[rows.to.plot],xlab="rho",ylab="gamma",type='p',main="rho v gamma",pch=".")
plot(posterior.samples$rho[rows.to.plot],posterior.samples$time.first.infected1[rows.to.plot],xlab="rho",ylab="time.first.infected1",type='p',main="rho v time.first.infected1",pch=".")
dev.off()
# calc stats - mean and 95% CIs for key quantities
# first chuck out first 1000 samples (i.e. 100,000 iterations) as a burnin
posterior.samples<-posterior.samples[1001: dim(posterior.samples)[1],]
#
# calc DIC
range<-10000:29000
dbar<- -2*mean(posterior.samples$LL[range])
#post.means<-data.frame(t(mean(posterior.samples)))
post.means<-data.frame(t(apply(posterior.samples[range,],2,mean)))[1:13]
# 1. Calculate DIC using the Spiegelhalter approach
dhat<- -2*getLLHepEmod.mh.combined.no.watsan(post.means, xstart1,xstart2,xstart3, plot=FALSE, SEIIR=TRUE)$LL
pD<-dbar-dhat
DIC<- dbar+pD
dbar
DIC
pD
# 2. Calculate DIC using the Gelman approach (invariant to reparameterisation so might be preferred)
p_v<- var(-2*posterior.samples$LL[range])
DIC2<- dbar+ p_v
DIC2
# 1. latent period
# mean
mean(365/posterior.samples$gamma)
quantile( 365/posterior.samples$gamma, c(.025,.5,.975))
# 2. infectious period
# mean
2*mean(365/posterior.samples$rho)
2*quantile( 365/posterior.samples$rho, c(.025,.5,.975))
# 3.proportion of infections which are symptomatic and reported
mean(posterior.samples$proportion.symptomatic)
quantile(posterior.samples$proportion.symptomatic, c(.025,.5,.975))
# 4.R0s for the three camps
mean(posterior.samples$R01)
quantile(posterior.samples$R01, c(.025,.5,.975))
mean(posterior.samples$R02)
quantile(posterior.samples$R02, c(.025,.5,.975))
mean(posterior.samples$R03)
quantile(posterior.samples$R03, c(.025,.5,.975))
# 5.Time of first infection for the three camps
365*mean(posterior.samples$time.first.infected1)
365*quantile(posterior.samples$time.first.infected1, c(.025,.5,.975))
365*mean(posterior.samples$time.first.infected2)
365*quantile(posterior.samples$time.first.infected2, c(.025,.5,.975))
365*mean(posterior.samples$time.first.infected3)
365*quantile(posterior.samples$time.first.infected3, c(.025,.5,.975))
# 6. dispersion parameter of negbin dist
mean(posterior.samples$disp)
quantile(posterior.samples$disp, c(.025,.5,.975))
# Plots of predicted v observed at each of the camps - start at week 27 2007 finish at week 26 2009
# First sample P runs for plotting randomly selected without replacement
P<-100
n.samples<-length(posterior.samples[,1])
runs.to.plot<- c(1:n.samples)[order(runif(n.samples))][1:P]
predicted1<-NULL
predicted2<-NULL
predicted3<-NULL
q.025prob.observed1<-NULL
q.975prob.observed1<-NULL
q.025prob.observed2<-NULL
q.975prob.observed2<-NULL
q.025prob.observed3<-NULL
q.975prob.observed3<-NULL
for(i in runs.to.plot){
weeks.from.infection.symptoms<-1
parameters<-posterior.samples[i,]
parameters1<-c(
beta.max=parameters$R01 *parameters$rho,
beta.min=parameters$R01 *parameters$rho, #assume no seasonality
phi=0, # phase angle of seasonal forcing in radians (specifies when peak occurs)
gamma1=parameters$gamma,
gamma2=parameters$gamma,
rho=parameters$rho
# r.water=0.000001,
# r.latrines=0.000001
)
parameters2<-c(
beta.max=parameters$R02 *parameters$rho,
beta.min=parameters$R02 *parameters$rho, #assume no seasonality
phi=0, # phase angle of seasonal forcing in radians (specifies when peak occurs)
gamma1=parameters$gamma,
gamma2=parameters$gamma,
rho=parameters$rho
# r.water=0.000001,
# r.latrines=0.000001
)
parameters3<-c(
beta.max=parameters$R03 *parameters$rho,
beta.min=parameters$R03 *parameters$rho, #assume no seasonality
phi=0, # phase angle of seasonal forcing in radians (specifies when peak occurs)
gamma1=parameters$gamma,
gamma2=parameters$gamma,
rho=parameters$rho
# r.water=0.000001,
# r.latrines=0.000001
)
time.first.infected1<-parameters$time.first.infected1
time.first.infected2<-parameters$time.first.infected2
time.first.infected3<-parameters$time.first.infected3
times1<- seq(ceiling(time.first.infected1*52)/52, 157/52, by = wk)
times2<- seq(ceiling(time.first.infected2*52)/52, 157/52, by = wk)
times3<- seq(ceiling(time.first.infected3*52)/52, 157/52, by = wk)
if(time.first.infected1!=times1[1]) times1<-c(time.first.infected1,times1)
if(time.first.infected2!=times2[1]) times2<-c(time.first.infected2,times2)
if(time.first.infected3!=times3[1]) times3<-c(time.first.infected3,times3)
# below should be same as out1 out2 and out3 calculated using the compiled code (and they ares)
#out1a<-ode(y=xstart1,times=times1, func=HepEmod.nowatsan,parameters1)
#out2a<-ode(y=xstart2,times=times2, func=HepEmod.nowatsan,parameters2)
#out3a<-ode(y=xstart3,times=times3, func=HepEmod.nowatsan,parameters3)
params1<-c(beta=parameters1[1],gamma=parameters1[4], rho=parameters1[5])
params2<-c(beta=parameters2[1],gamma=parameters2[4], rho=parameters2[5])
params3<-c(beta=parameters3[1],gamma=parameters3[4], rho=parameters3[5])
# out1<-ode(y=xstart1,times=times1, func="derivs",parms=params1,jacfun="jac",dllname="SEIR", initfunc="initmod",nout=1,outnames="Sum")
# out2<-ode(y=xstart2,times=times2, func="derivs",parms=params2,jacfun="jac",dllname="SEIR", initfunc="initmod",nout=1,outnames="Sum")
#out3<-ode(y=xstart3,times=times3, func="derivs",parms=params3,jacfun="jac",dllname="SEIR", initfunc="initmod",nout=1,outnames="Sum")
out1<-ode(y=xstart1,times=times1, func="derivs",parms=params1,jacfun="jac",dllname="SEEIR", initfunc="initmod",nout=1,outnames="Sum")
out2<-ode(y=xstart2,times=times2, func="derivs",parms=params2,jacfun="jac",dllname="SEEIR", initfunc="initmod",nout=1,outnames="Sum")
out3<-ode(y=xstart3,times=times3, func="derivs",parms=params3,jacfun="jac",dllname="SEEIR", initfunc="initmod",nout=1,outnames="Sum")
cuminc1<-out1[,6][-1] # the [-1] drops the first time point for cuminc, so we start counting at exact times of each new week
cuminc2<-out2[,6][-1] # the [-1] drops the first time point for cuminc, so we start counting at exact times of each new week
cuminc3<-out3[,6][-1] # the [-1] drops the first time point for cuminc, so we start counting at exact times of each new week
obs1<-OBSERVED.CASES1[27:130] # data from week 27 2007 to week 26 2009
obs2<-OBSERVED.CASES2[27:130] # data from week 27 2007 to week 26 2009
obs3<-OBSERVED.CASES3[27:130] # data from week 27 2007 to week 26 2009
n1<-length(cuminc1)
n2<-length(cuminc2)
n3<-length(cuminc3)
# first remove weeks 131 to 157 from cuminc i.e. the last 27 ob
cuminc1<-cuminc1[1:(n1-27)]
cuminc2<-cuminc2[1:(n2-27)]
cuminc3<-cuminc3[1:(n3-27)]
n1<-length(cuminc1)
n2<-length(cuminc2)
n3<-length(cuminc3)
weeklyinc1<-c(cuminc1[1],cuminc1[2:n1]-cuminc1[1:(n1-1)]) # weekly incidence
weeklyinc2<-c(cuminc2[1],cuminc2[2:n2]-cuminc2[1:(n2-1)]) # weekly incidence
weeklyinc3<-c(cuminc3[1],cuminc3[2:n3]-cuminc3[1:(n3-1)]) # weekly incidence
n1<-length(cuminc1)
n2<-length(cuminc2)
n3<-length(cuminc3)
wk.inc1<-weeklyinc1[1:(n1-weeks.from.infection.symptoms)] # this gives total incident infectious caes - a proportion of whcih will be symptomatic & reported after a delay of weeks.from.infection.symptoms
wk.inc2<-weeklyinc2[1:(n2-weeks.from.infection.symptoms)] # this gives total incident infectious caes - a proportion of whcih will be symptomatic & reported after a delay of weeks.from.infection.symptoms
wk.inc3<-weeklyinc3[1:(n3-weeks.from.infection.symptoms)] # this gives total incident infectious caes - a proportion of whcih will be symptomatic & reported after a delay of weeks.from.infection.symptoms
n1<-length(wk.inc1)
n2<-length(wk.inc2)
n3<-length(wk.inc3)
firstwk<-ceiling(time.first.infected1*52) + weeks.from.infection.symptoms # first week where we have cuminc data
if(firstwk>27){
wk.inc1 <- c(rep(0,104-n1), wk.inc1)
}
if(firstwk<27){
wk.inc1 <- wk.inc1[(28-firstwk):n1]
}
firstwk<-ceiling(time.first.infected2*52) + weeks.from.infection.symptoms # first week where we have cuminc data
if(firstwk>27){
wk.inc2 <- c(rep(0,104-n2), wk.inc2)
}
if(firstwk<27){
wk.inc2 <- wk.inc2[(28-firstwk):n2]
}
firstwk<-ceiling(time.first.infected3*52) + weeks.from.infection.symptoms # first week where we have cuminc data
if(firstwk>27){
wk.inc3 <- c(rep(0,104-n3), wk.inc3)
}
if(firstwk<27){
wk.inc3 <- wk.inc3[(28-firstwk):n3]
}
predicted1<- rbind(predicted1,parameters$proportion.symptomatic*wk.inc1)
predicted2<- rbind(predicted2,parameters$proportion.symptomatic*wk.inc2)
predicted3<- rbind(predicted3,parameters$proportion.symptomatic*wk.inc3)
# binomial likelihood
# q.025prob.observed1<-rbind(q.025prob.observed1,qbinom(.025,round(wk.inc1),parameters$proportion.symptomatic))
# q.975prob.observed1<-rbind(q.975prob.observed1,qbinom(.975,round(wk.inc1),parameters$proportion.symptomatic))
# q.025prob.observed2<-rbind(q.025prob.observed2,qbinom(.025,round(wk.inc2),parameters$proportion.symptomatic))
# q.975prob.observed2<-rbind(q.975prob.observed2,qbinom(.975,round(wk.inc2),parameters$proportion.symptomatic))
# q.025prob.observed3<-rbind(q.025prob.observed3,qbinom(.025,round(wk.inc3),parameters$proportion.symptomatic))