Global Dynamics of an SEIR Model with Two Age Structures and a Nonlinear Incidence

In this paper, we study an SEIR model with both infection and latency ages and also a very general class of nonlinear incidence. We first present some preliminary results on the existence of solutions and on bounds of solutions. Then we study the global dynamics in detail. After proving the existence of a global attractor A, we characterize it in two cases distinguished by the basic reproduction number R0. When R0<1, we apply the Fluctuation Lemma to show that the disease-free equilibrium E0 is globally asymptotically stable, which means A={E0}. When R0>1, we show the uniform persistence and get A={E0}CA1, where C consists of points with connecting orbits from E0 to A1 and A1 attracts all points with initial infection force. Under an additional condition, we employ the approach of Lyapunov functional to find that A1 just consists of an endemic equilibrium.

Automated summary

The paper investigates an SEIR model with infection and latency ages as well as a general class of nonlinear incidence. It presents preliminary results on existence of solutions and bounds of solutions, then delves into global dynamics. The existence of a global attractor A is proven, characterized by cases of basic reproduction number R0 less than or greater than 1, demonstrating stability and persistence properties. The approach of Lyapunov functional is employed to identify an endemic equilibrium in the case of R0>1.