Dynamics Of An Sirs Model With Age Structure And Two Delays

In this paper, we propose and investigate an SIRS model with age structure and two delays. Both the infected and the recovered individuals have age structure, the infection rate (from the infective to the susceptible) and the immune loss rate (from the recovered to the susceptible) are related to two independent time delays, respectively. We prove that the proposed age structured SIRS model is well-posed by using the C-0-semigroup theory. The basic reproduction number R-0 is given, and the unique endemic equilibrium exists when R-0 > 1, while the disease-free equilibrium always exists. A rigorous mathematical analysis for the stability of two equilibria is provided. The disease-free equilibrium is local asymptotically stable if R-0 < 1, and the endemic equilibrium is local asymptotically stable if R-0 > 1 and tau l = 0. Finally, we give numerical simulations to verify our results.