In this talk, we propose and analyze an SIRI epidemic model infection age and a general nonlinear incidence rate. Established is a threshold dynamics determined by the basic reproduction number R0.
Roughly speaking, if R0 < 1 then the disease-free steady state is glob-ally asymptotically stable while if R0 > 1 then the endemic steady state is globally asymptotically stable. The global attractivity for the steady states are obtained by employing the fluctuation lemma and the approach of Lyapunov functionals. Our results imply that decreasing the initial transmission rate and drawing up efficient prevention ways play a much more important role on controlling the disease spread than increasing the total treatment rate. The obtained theoretical results are illustrated with numerical simulations, which also indicate that infection age is an im-portant factor affecting the epidemic spread. This is a joint work with Junyuan Yang and Toshikazu Kuniya.