STABILITY AND PERSISTENCE OF A SEIRS MODEL WITH MULTIPLE AGES AND DELAY

This paper focuses on the dynamical behavior of an age-structured epidemic model including a nonlinear incidence and immune loss. For this the well-posedness of the considered model is obtained and the existence of the equilibria is obtained. Then the stability and persistence problems are investigated for this system. More precisely, the disease-free equilibrium is globally asymptotically stable when the basic reproduction number R0 < 1, while if R0 > 1, the solutions of the system are uniformly persist and the positive equilibrium has locally asymptotical stability. Additionally a simple three-way partition for the global attractor of the solution semi-flow for the considered system is also obtained. In the end some numerical simulations are provided to illustrate the obtained theoretical results.