Statistical Modelling 4 (2004), 6375
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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