Global stability of an information-related epidemic model with age-dependent latency and relapse

We study the problem of information-related contact rate for an SEIR epidemic model with age-dependent latency and relapse. The contact pattern includes an information variable which is a negative feedback of susceptible individuals related to the memory of past and current states of infectious disease. We prove the asymptotic smoothness of solutions and the existence of equilibria in the positive invariant set. And we show uniform persistence of the system by comparing with a system of Volterra type integro-differential equations. Importantly, it follows from appropriate conditions that the local stability and global stability of equilibria can be concluded by the methods of corresponding characteristic equations and proper Lyapunov functionals, respectively. Finally, we give numerical simulations to illustrate the influence of the information on changing the coordinate of endemic equilibrium by increasing susceptible population and decreasing infectious population. It is remarkable to find that information coverage and the length of disease-relate memory would work effectively on the progression of disease.