Modeling diseases with latency and nonlinear incidence rates: global dynamics of a multi-group model

摘要

In this paper, we perform global stability analysis of a multi-group SEIR epidemic model in which we can consider the heterogeneity of host population and the effects of latency and nonlinear incidence rates. For a simpler version that assumes an identical natural death rate for all groups, and with a gamma distribution for the latency, the basic reproduction number is defined by the theory of the next generation operator and proved to be a sharp threshold determining whether or not disease spread. Under certain assumptions, the disease-free equilibrium is globally asymptotically stable if R(0)1 and there exists a unique endemic equilibrium which is globally asymptotically stable if R-0>1. The proofs of global stability of equilibria exploit a matrix-theoretic method using Perron eigenvetor, a graph-theoretic method based on Kirchhoff's matrix tree theorem and Lyapunov functionals. Copyright (c) 2015 John Wiley & Sons, Ltd.