Global analysis of an age-structured SEIR model with immigration of population and nonlinear incidence rate

Epidemic models with infection age of infectious individuals have been extensively studied, however, most of the existing works ignore the combined effects of immigration and nonlinear incidence. In this paper, we incorporate both the effects of immigration and nonlinear incidence, based on which we formulate an SEIR epidemic model. We give a rigorous mathematical analysis on some necessary technical materials. Then, by constructing a Lyapunov functional, we show that the endemic equilibrium is globally asymptotically stable. Numerical simulations of an application are given to support our theoretical results.