Bubonic plague (Yersinia pestis) is generally thought of as an
historical disease, however it is still responsible for around one to three
thousand deaths each year worldwide. This paper expands the analysis of
a model for bubonic plague that encompasses the disease dynamics in rat,
flea and human populations. Some key variables of the deterministic model,
including the force of infection to humans, are shown to be robust to changes
in the basic parameters, although variation in the flea searching efficiency,
and the movement rates of rats and fleas will be considered throughout
the paper. The stochastic behaviour of the corresponding metapopulation
model is discussed, with attention focused on the dynamics of rats and
the force of infection at the local spatial scale. Short-lived local epidemics
in rats govern the invasion of the disease and produce an irregular pattern
of human cases similar to those observed. However, the endemic behaviour
in a few rat subpopulations allows the disease to persist for many years.
This spatial stochastic model is also used to identify the criteria for
the spread to human populations in terms of the rat density. Finally, the
full stochastic model is reduced to the form of a probabilistic cellular
automaton, which allows the analysis of a large number of replicated epidemics
in large populations. This simplified model enables us to analyse the spatial
properties of rat epidemics and the effects of movement rates, as well
as to test whether the emergent metapopulation behaviour is a property
of the local dynamics rather than the precise details of the model.