Analysis of Dynamics of a Recurrent Infectious Disease SIRS Model with Age Structure and Two Delays

Abstract

In this paper, an SIRS model with age structure is proposed for recurrent infectious diseases by incorporating infectious delay and temporary immunity delay. Analysis shows that the disease will eventually disappear when the basic reproduction number [Formula: see text]. No matter how the infection delay [Formula: see text] changes, as long as the temporary immunity loss delay [Formula: see text], the disease transmission will only be endemic and there will be no periodic oscillations when [Formula: see text]. Moreover, the stability and Hopf bifurcation will appear as [Formula: see text] increases from zero. It indicates that the duration of temporary immunity can affect the form of disease transmission within the population. Our numerical simulations verified the correctness of the theoretical results.