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Mathematical Biosciences and Engineering

2012, Volume 9, Issue 3: 685-695. doi: 10.3934/mbe.2012.9.685
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Global properties of a delayed SIR epidemic model with multiple parallel infectious stages

  • 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: 01 October 2011 Accepted: 29 June 2018 Published: 01 July 2012

  • MSC : 34C05, 92D25.

  • 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 $R_0>1$.

    Citation: Xia Wang, Shengqiang Liu. Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages[J]. Mathematical Biosciences and Engineering, 2012, 9(3): 685-695. doi: 10.3934/mbe.2012.9.685

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  • 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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  • © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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