Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates
Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates
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DOI：
10.1016/j.amc.2011.11.016
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发表时间：
2012
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影响因子：
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通讯作者：
Yoichi Enatsu;E. Messina;Y. Muroya;Y. Nakata;E. Russo;A. Vecchio
中科院分区：
文献类型：
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作者：
Yoichi Enatsu;E. Messina;Y. Muroya;Y. Nakata;E. Russo;A. Vecchio
分析了一类时滞SIR传染病模型平衡点的稳定性，其中无病人口增长服从Logistic增长，且非线性感染率满足适当的单调性条件。该模型存在唯一的地方病平衡点当且仅当基本繁殖数R0大于1时，平凡平衡点和无病平衡点始终存在。首先，我们证明了无病平衡点是全局渐近稳定的当且仅当R0⩽1。其次，我们证明了该模型是持久的当且仅当R0>；1。此外，利用以非线性关联函数为特征的阈值参数R‘0，我们证明了地方病平衡点是局部渐近稳定的，并且当时滞长度超过1<；R0<；R0的临界值时，它失去稳定性。我们的结果推广了[J.-J.Wang，J.-Z.Zhang，Z.jin，Analysis of an SIR Model with双线性传染病，非线性分析]中的稳定性结果。RWA 11(2009)2390-2402]。
We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R0exceeds one, while the trivial equilibrium and the disease-free equilibrium always exist. First we show that the disease-free equilibrium is globally asymptotically stable if and only if R0⩽1. Second we show that the model is permanent if and only if R0>1. Moreover, using a threshold parameter R¯0characterized by the nonlinear incidence function, we establish that the endemic equilibrium is locally asymptotically stable for 1<R0⩽R¯0and it loses stability as the length of the delay increases past a critical value for 1<R¯0<R0. Our result is an extension of the stability results in [J.-J. Wang, J.-Z. Zhang, Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonlinear Anal. RWA 11 (2009) 2390–2402].