A Host-Host-Pathogen Model with Vaccination and its Application to Target and Reservoir Hosts

Abstract

In this paper we present a simple theoretical framework which allows us to study the impact of constant vaccination rates in a system in which two species interact through a shared pathogen. We look at this firstly in purely theoretical terms to determine which equilibria will be stable for which parameter combinations. We then consider two special cases and determine the long term population dynamical consequences of differing vaccination strategies. In particular we describe systems for which there is a wildlife host reservoir and a domestic (target) host. We find that when the target host cannot maintain the disease alone, and the presence of the reservoir causes the target host to be eradicated by the disease, vaccinating the target species allows coexistence of the two species with the pathogen, but will not allow disease eradication. It is then shown that this result holds both when vaccination occurs at a fixed rate and when a proportion of the population is vaccinated at birth.