Carrier-borne epidemics with immigration. I — Immigration of both susceptibles and carriers

Abstract

Much of the theory of epidemics (see Bailey, 1957) has been concerned with models for their behaviour in closed populations. In such models the epidemic ultimately dies out, and interest has been concentrated on, for example, the ultimate size of the epidemic and its duration in time. In practice a population is rarely completely closed, and for many diseases an endemic model rather than an epidemic model is appropriate. To create models for endemic diseases it is necessary to introduce both new persons susceptible to the disease into the population and new sources of infection. For the so-called general stochastic epidemic, Ridler-Rowe (1967) has obtained certain limiting properties of the population where immigration of both susceptibles and infectives into the population takes place, but much work remains to be done to obtain, for example, the general equilibrium behaviour of this model.