Disease Incidence in a Stochastic SVIRS Model with Waning Immunity

Abstract

This paper deals with the long-term behaviour and incidence of a vaccine-preventable contact disease, under the assumption that both vaccine protection and immunity after recovery are not lifelong. The mathematical model is developed in a stochastic markovian framework. The evolution of the disease in a finite population is thus represented by a three-dimensional continuous-time Markov chain, which is versatile enough to be able to compensate for the loss of protection by including vaccination before the onset of the outbreak and also during the course of the epidemics.