Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages

Xia Wang; Shengqiang Liu

doi:10.3934/mbe.2012.9.685

Article Contents

2012, Volume 9, Issue 3: 685-695. Doi: 10.3934/mbe.2012.9.685

This issue Previous Article A minimal mathematical model for the initial molecular interactions of death receptor signalling Next Article Erratum to: Investigating the steady state of multicellular sheroids by revisiting the two-fluid model

Global properties of a delayed SIR epidemic model with multiple parallel infectious stages

Xia Wang^1, and
Shengqiang Liu^2,

1.
Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street Harbin, 150080 and College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000
2.
Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Harbin, 150080

Received: October 2011

Revised: February 2012

Published: June 2012

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Abstract

In this paper, we study the global properties of an SIR epidemic model with distributed delays, where there are several parallel infective stages, and some of the infected cells are detected and treated, which others remain undetected and untreated. The model is analyzed by determining a basic reproduction number $R_0$, and by using Lyapunov functionals, we prove that the infection-free equilibrium $E^0$ of system (3) is globally asymptotically attractive when $R_0\leq 1$, and that the unique infected equilibrium $E^*$ of system (3) exists and it is globally asymptotically attractive when $R_0>1$.

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Mathematics Subject Classification: 34C05, 92D25.

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