title: Global dynamics of a general class of multi-group epidemic models with latency and relapse.
abstract: A multi-group model is proposed to describe a general relapse phenomenon of infectious diseases in heterogeneous populations. In each group, the population is divided into susceptible, exposed, infectious, and recovered subclasses. A general nonlinear incidence rate is used in the model. The results show that the global dynamics are completely determined by the basic reproduction number R0. In particular, a matrix-theoretic method is used to prove the global stability of the disease-free equilibrium when R0 ≤ 1, while a new combinatorial identity (Theorem 3.3 in Shuai and van den Driessche) in graph theory is applied to prove the global stability of the endemic equilibrium when R0 > 1. We would like to mention that by applying the new combinatorial identity, a graph of 3n (or 2n+m) vertices can be converted into a graph of n vertices in order to deal with the global stability of the endemic equilibrium in this paper.
authors: College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China. xiaomei_0529@126.com.
authors: Xiaomei
authors: X
authors: Feng
authors: Zhidong
authors: Z
authors: Teng
authors: Fengqin
authors: F
authors: Zhang
mesh_terms: D000465:Algorithms; D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology*; D003198:Computer Simulation; D058872:Epidemics; D006801:Humans; D015233:Models, Statistical; D012008:Recurrence