A bivariate birth-death process which approximates to the spread of a disease involving a vector

Abstract

A simple model for a bivariate birth-death process is proposed. This model approximates to the host-vector epidemic situation. An investigation of the transient process is made and the mean behaviour over time is explicitly found. The probability of extinction and the behaviour of the process conditional upon extinction are examined and the probability distribution of the cumulative population size to extinction is found. Appropriate circumstances are suggested under which the model might possibly be applied to malaria. The host-vector model is classified within a general class of models which represent large population approximations to epidemics involving two types of infectives.