A Consistent Discrete Version of a Nonautonomous SIRVS Model

Abstract

A family of discrete nonautonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens nonstandard discretization method. Conditions for the permanence and extinction of the disease and the stability of disease-free solutions are determined. Concerning extinction and persistence, the consistency of those discrete models with the corresponding continuous model is discussed: if the time step is sufficiently small, when we have extinction (permanence) for the continuous model, we also have extinction (permanence) for the corresponding discrete model. Some numerical simulations are carried out to compare the different possible discretizations of our continuous model using real data.