Abstract

The threshold theorem for deterministic epidemics in mixing populations can usually be rewritten in such a form that a large epidemic results from trace infection if and only if , where can be interpreted as a basic reproduction ratio for an associated population model. The Whittle stochastic threshold theorem replaces certainty with probability: if , a large epidemic is highly unlikely to result from the introduction of one or two infectives, whereas, if , the probability of having a significant epidemic is no longer trivial. In this paper, the Whittle approximation to a model for parasitic infection in a mixing population is analysed. A feature of the model is that is well defined, but for certain parameter values the threshold is not at . Thus to have as threshold for epidemics in mixing populations is by no means a universal rule. A related birth and death process with drift is also investigated.