Global stability for a multi-group SIRS epidemic model with varying population sizes

a b s t r a c tIn this paper, to analyze the effect of the cross patch infection between different groups to the spread of gonorrhea in a community, we establish the complete global dynamics of a multigroup SIS epidemic model with varying total population size by a threshold parameter. In the proof, we use special Lyapunov functional techniques, not only one proposed by the paper [Prüss et al., 2006], but also the other one for a varying total population size with some ideas specified to our model and no longer need a grouping technique derived from the graph theory which is commonly used for the global stability analysis of multi-group epidemic models.

show abstract

“…We note that thisR 0 corresponds to the basic reproduction number R 0 of (1.1) (see for example, [23] and [33]). …”

Section: Introductionmentioning

confidence: 94%

Global stability of a multi-group SIS epidemic model with varying total population size

Kuniya

Muroya

2015

Applied Mathematics and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…, υ n ) corresponding to the spectral radius ρ(F 1 B) = R 0 > 0. Motivated by [25,29,26], consider a Lyapunov function for model (1)…”

Section: Xiaomei Feng Zhidong Teng and Fengqin Zhangmentioning

confidence: 99%

“…Groups can be geographical such as communities, cities, and countries, or epidemiological, to incorporate differential infectivity or co-infection of multiple strains of the disease agent. There has been much research on multigroup epidemic models, for example, see [6,15,20,25,28,32,26] and references therein. The question of global stability in higher dimensions models is always a challenging and difficult task.…”

mentioning

confidence: 99%

Global dynamics of a general class of multi-group epidemic models with latency and relapse

Feng

Teng²,

Zhang

2015

Mathematical Biosciences and Engineering

View full text Add to dashboard Cite

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.

show abstract

“…Van den Driessche et al [1,2] proposed a mathematical model for a disease with a general exposed distribution and the possibility of relapse. Because multiple strain models [3], multi-group models [4] and multi-patch models [5] are frequently used in population dynamics, great attention has also been paid to such epidemic models [7][8][9][10][11], recently. Motivated by these works, we propose in this paper a multi-group epidemic model with two distributed delays (latency and relapse) and with a general nonlinear incidence function F.S, I/, which extends and improves some known epidemic models with relapse [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Threshold dynamics of a nonlinear multi‐group epidemic model with two infinite distributed delays

Feng

Wang

Zhang

et al. 2016

Math Methods in App Sciences

View full text Add to dashboard Cite

The global stability of equilibria is investigated for a nonlinear multi‐group epidemic model with latency and relapses described by two distributed delays. The results show that the global dynamics are completely determined by the basic reproduction number scriptR0 under certain reasonable conditions on the nonlinear incidence rate. Moreover, compared with the results in Michael Y. Li and Zhisheng Shuai, Journal Differential Equations 248 (2010) 1–20, it is found that the two distributed delays have no impact on the global behaviour of the model. Our study improves and extends some known results in recent literature. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

Global stability for a multi-group SIRS epidemic model with varying population sizes

Cited by 77 publications

References 17 publications

Global stability of a multi-group SIS epidemic model with varying total population size

Global stability of a multi-group SIS epidemic model with varying total population size

Global dynamics of a general class of multi-group epidemic models with latency and relapse

Threshold dynamics of a nonlinear multi‐group epidemic model with two infinite distributed delays

Contact Info

Product

Resources

About