The effect of incubation time distribution on the extinction characteristics of a rabies epizootic

The continuous model of Anderson et al. (1981), Nature 289, 765–771, is successful in describing certain characteristics of rabies epizootics, in particular, the secondary recurrences which follow the initial outbreak; however, it also predicts the occurrence of exponentially small minima in the infected population, which would realistically imply extinction of the virus. Here we show that inclusion of a more realistic distribution of incubation times in the model can explain why extinction will not occur, and we give explicit parametric estimates for the minimum infected fox density which will occur in the model, in terms of the incubation time distribution.