A Generalized Non-Autonomous SIRVS Model

Abstract

A non-autonomous SIRVS epidemic model, with incidence rates are represented by functions ϕ(t, S)I and ψ(t,V )I, where S, I and V stand for the Susceptible, Infective and Vaccinated populations respectively, is proposed. The global dynamics of the system is investigated and sufficient conditions for the permanence and extinction of the infection are obtained. In particular numbers to measure the force of infection in terms of the threshold conditions are provided. Numerical simulations are performed to validate the analytical theory. Examples with periodic functions are used to describe phenomena of common diseases.