The basic reproduction number in some discrete-time epidemic models

Abstract

The next generation matrix approach for calculating the basic reproduction number is summarized for discrete-time epidemic models. This approach is applied to six disease models developed for the study of two emerging wildlife diseases: hantavirus in rodents and chytridiomycosis in amphibians. Two of the models include discrete spatial patches. For each model, is calculated in terms of the model parameters. For , if a small number of infectives is introduced, then the wildlife disease dies out. Global stability of the disease-free equilibrium is verified for a special case of the SI hantavirus model when . In addition, a numerical example indicates that there is a transcritical bifurcation at , with the disease dying out if but tending to an endemic level if .