GLOBAL DYNAMICS OF A GENERAL CLASS OF MULTI-GROUP EPIDEMIC MODELS WITH LATENCY AND RELAPSE
GLOBAL DYNAMICS OF A GENERAL CLASS OF MULTI-GROUP EPIDEMIC MODELS WITH LATENCY AND RELAPSE
复制标题
具有潜伏期和复发的一般类多组流行病模型的全局动态。
DOI：
10.3934/mbe.2015.12.99
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发表时间：
2015-02-01
影响因子：
2.6
通讯作者：
Zhang, Fengqin
中科院分区：
文献类型：
--
作者：
Feng, Xiaomei;Teng, Zhidong;Zhang, Fengqin
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.
