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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

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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Keywords distributed delay; global attractivity; Lyapounov functional.; SIR epidemic model

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

 

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