Statistical Modelling 4 (2004), 63–75

Bayesian inference for stochastic epidemics in closed populations

George Streftaris
Actuarial Mathematics and Statistics
School of Mathematical and Computer Sciences
Heriot-Watt University, Riccarton
Edinburgh EH14 4AS
UK.
eMail: g.streftaris@ma.hw.ac.uk

Gavin J. Gibson
Actuarial Mathematics and Statistics
School of Mathematical and Computer Sciences
Heriot-Watt University, Riccarton
Edinburgh EH14 4AS
UK.
eMail: g.j.gibson@ma.hw.ac.uk

Abstract:

We consider continuous-time stochastic compartmental models which can be applied in veterinary epidemiology to model the within-herd dynamics of infectious diseases. We focus on an extension of Markovian epidemic models, allowing the infectious period of an individual to follow a Weibull distribution, resulting in a more flexible model for many diseases. Following a Bayesian approach we show how approximation methods can be applied to design efficient MCMC algorithms with favourable mixing properties for fitting non-Markovian models to partial observations of epidemic processes. The methodology is used to analyse real data concerning a smallpox outbreak in a human population, and a simulation study is conducted to assess the effects of the frequency and accuracy of diagnostic tests on the information yielded on the epidemic process.

Keywords:

Bayesian inference; diagnostic tests; Markov chain Monte Carlo; Metropolis--Hastings acceptance rate; non-Markovian model; stochastic epidemic modelling.
 

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