Bubonic plague: a metapopulation model of a zoonosis

Bubonic plague (Yersinia pestis) is generally thought of as a historical di sease; however, it is still responsible for around 1000 -3000 deaths each y ear worldwide. This paper expands the analysis of a model for bubonic plagu e that encompasses the disease dynamics in rat, flea and human populations. Some key variables of the the deterministic model, including the force of infection to humans, are shown to be robust to changes ill the basic parame ters, although variation in the flea searching efficiency and the movement rates of rats and fleas will be considered throughout the pal,cr. The stoch astic behaviour of the corresponding metapopulation model is discussed, wit h attention focused on the dynamics of rats and the force of infection at t he local spatial scale. Short-lived local epidemics in rats govern the inva sion of the disease and produce an irregular pattern of human cases similar to those observed. However; the endemic behaviour in a few rat subpopulati ons allows the disease to persist for many years. This spatial stochastic m odel is also used to identify the criteria for the spread to human populati ons in terms of the rat density. Finally, the full stochastic model is redu ced to the form of a probabilistic cellular automaton, which allows the ana lysis of a large number of replicated epidemics in large populations. This simplified model enables us to analyse the spatial properties of rat epidem ics and the effects of movement rates, and also to test whether the emergen t metapopulation behaviour is a property of the local dynamics rather than the precise details of the model.