SEIR.MH {stochasticGEM}R Documentation

Fit a partially observed SEIR general epidemic model.

Description

SEIR.MH is used to fit the SEIR general epidemic model via Markov chain Monte Carlo. In this compartmental model only the removal times are observed. The computation is based on the algorithm that is developed by O`Neill & Becker (2001).

Usage

SEIR.MH(N, infectionTimes = NULL, InfPeriod = c(1,20), 
    latencyTimes = NULL, LatPeriod = c(1,20), removalTimes,  START = NULL, 
    priorValues = NULL, bayesReps = 10000, burnIn = 0, bayesThin = 1, 
    verbose = FALSE, missingInfectionTimes = TRUE)

Arguments

N initial susceptible individuals
infectionTimes removal times
InfPeriod A range of giving the possible infectious periods
latencyTimes end of latency times
LatPeriod A range of giving the possible latency durations
removalTimes removal times
START A vector with 2 elements, the infection and removal rate respectively. Defaults to NULL.
priorValues A list with elementsinfectionRate, removalRate and theta, the first 2 being vectors of length 2 containing the gamma prior coefficients for the corresponding parameters, and theta being a scalar for the exponential prior of the infection time of the initial infective. Defaults to NULL.
bayesReps A positive integer denoting the number of MCMC draws. The default is 10000
burnIn A positive integer denoting the burn-in interval for the Markov chain, i.e., the number of initial draws that should not be stored. The default is 0.
bayesThin A positive integer denoting the thinning interval for the Markov chain, i.e., the interval between successive values of the Markov chain. The default is 1.
verbose Used to check activity of MCMC sampler. A dot is printed at every bayesReps/100 iteration.
missingInfectionTimes Are missing values updated or fixed. By default the infection times are updated.

Details

If certain elements of the starting values are missing an attempt is made to get suitable starting values.

Value

a list of components containing the folowing elements:

logLikelihood A Markov chain Monte Carlo object of the 'psuedo' log likelihood for each completed data set. The function mcmc in the coda library is used to create the object.
infectionTimes Posterior mean of the infection times.
removalTimes Removal times.
infRateSEIR A Markov chain Monte Carlo object of the Gibbs draws for the infection rate. The function mcmc in the coda library is used to create the object.
latRateSEIR A Markov chain Monte Carlo object of the Gibbs draws for the latency rate. The function mcmc in the coda library is used to create the object.
remRateSEIR A Markov chain Monte Carlo object of the Gibbs draws for the removal rate. The function mcmc in the coda library is used to create the object.
acceptRate Number of accepted draws for the infection times.
bayesReps The number of MCMC draws
burnIn The burn-in interval for the Markov chain.
bayesThin The thinning interval for the Markov chain.
bayesOut Number of saved iterations.
infectiousPeriod A Markov chain Monte Carlo object of the infectious period. The function mcmc in the coda library is used to create the object.
reproductionNumber A Markov chain Monte Carlo object of the reproduction number. The function mcmc in the coda library is used to create the object.
initialSusceptible Initial susceptible individuals.
initialInfective Initial infective individuals.

Author(s)

Eugene Zwane e.zwane@gmail.com

References

Gibson, G.J. & Renshaw, E. (1998). 'Estimating the parameters in stochastic epidemic models using Markov chain models' IMA Journal of Mathematics Applied in Medicine & Biology 16, 19-40.

Hoehle, M., Jorgensen, E. & O'Neill, P.D. (2005). 'Inference in disease transmission experiments by using stochastic epidemic models' Appl. Statist. 54, 349-366.

O'Neill, P.D. & Roberts, G.O. (1999). 'Bayesian inference for partially observed stochastic epidemics' J.R. Statist. Soc. A. 162, 121-129.

O'Neill, P.D. & Becker, N.G. (2001). 'Inference for an epidemic when susceptibility varies' Biostatistics 2, 99-108.

O'Neill, P.D. (2002). 'A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods' Mathematical Biosciences 180, 103-114.

See Also

fLatentSEIR.MH, getValidSEIR, SIR.MH, SIR.MLE

Examples

 
        data(smallpox) 
        priors <- list(infectionRate = c(1.00,0.01),
                latencyRate = c(1.00,0.01),
                removalRate = c(1.00,0.01), 
                theta = c(0.01,0.01))
        validStartTimes <- getValidSEIR(119,smallpox,13)
        temp <- SEIR.MH(N=119,
                infectionTimes=validStartTimes$infectionTimes,
                latencyTimes=validStartTimes$latencyTimes,
                removalTimes=smallpox, priorValues=priors,
                bayesReps=1000,burnIn=500,bayesThin=1)
        summary(temp$infRateSEIR)
        summary(temp$remRateSEIR)
        summary(temp$infectiousPeriod)
        summary(temp$reproductionNumber)

[Package stochasticGEM version 0.0-1 Index]