Estimating Parameters for Stochastic Epidemics
Michael H÷hle, Department of Animal Science and Animal Health, Royal Veterinary and Agricultural University, Denmark
Erik J°rgensen, Department of Agricultural Systems, Danish Institute of Agricultural Sciences, Research Centre Foulum, Denmark
Understanding the spread of infectious disease is an important issue in order to prevent major outbreaks. In this report mathematical modeling is used to gain insight into the dynamics of an epidemic. A process model, the SIR model, exploiting knowledge about population dynamics serves as framework. Key interest is in adapting the stochastic model to observed data -- especially from animal production. Observing all events of an epidemic is not feasible in practice, hence estimation of model parameters has to be done from missing data. We give a rigorous treatment of an existing technique to handle estimation in partially observed epidemics using Markov Chain Monte Carlo (MCMC). The aim of this report is to extend the basic SIR model to handle two common situations in animal production: interaction into the course of the epidemic and population heterogeneity due to the spatial layout of confinement. Handling partially observed epidemics in these contexts we do by extending the above described MCMC method. A programming environment has been developed to exemplify the model extensions at a proof of concept level. It is made available for download for others to confirm our results or try the extensions on their own data.
Infectious disease, SIR model, partial observability, Markov chain Monte Carlo, multi-type epidemic.