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

Abstract

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 R0≤1 and there exists a unique endemic equilibrium which is globally asymptotically stable if R0>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 © 2015 John Wiley & Sons, Ltd.

Mathematical analysis for a multi-group SEIR epidemic model with age-dependent relapse

“…The global stability analysis of endemic equilibrium of such models has been studied by a novel approach using the graph theory, see as in [6,7,14]. Recently, diseases with latency and relapse have been included in multi-group epidemic models in [11,[30][31][32].…”

Threshold dynamics of a delayed multi-group heroin epidemic model in heterogeneous populations

“…The global dynamics of equilibria of multi-group models involving basic reproduction number and a graph-theoretic approach to the method of global Lyapunov functionals can be found in the literatures. We refer to [6,10,19,20,3,16,17,25,9,24,26,23] and references therein.…”