Asymptotic Behavior of an Infection-age-dependent SIS Epidemic Model with General Form Nonlinear Saturated Infectivity

Dynamical behavior of an infection-age-dependent SIS epidemic model with general form nonlinear saturated infectivity is studied and the threshold, a basic reproductive number which determines the outcome of the infectious disease is found. When the basic reproduc- tive number is not greater than 1 meaning the disease will be extinct, there exists only a disease-free equilibrium, which is globally asymptotically stable except that the basic repro- ductive number equals 1. When the basic reproductive number is greater than 1 meaning the disease will persist, there are two equilibria, the disease-free equilibrium which is un- stable and the endemic equilibrium which is locally asymptotically stable. The previous ODE model can be viewed as especial example and its relevant results can be regarded as corollaries of this article.