On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate
On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate
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DOI：
10.1016/j.amc.2010.10.007
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发表时间：
2010-12
期刊：
影响因子：
--
通讯作者：
B. Buonomo;S. Rionero
中科院分区：
文献类型：
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作者：
B. Buonomo;S. Rionero
研究了一类具有非永久获得性免疫（SIRS）的传染病模型。发病率被假定为一个一般的非线性函数的易感性和传染类。通过使用特殊的李雅普诺夫函数，得到了平衡点局部非线性稳定的充分必要条件。同时也得到了保证全局稳定的条件。与最近关于这一主题的文献不同，这里不需要关于传染病类别的发病率的单调性和单调性的限制。在这些应用中，提供了值得注意的凸发生率案例。
We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be a general nonlinear function of the susceptibles and the infectious classes. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability are also obtained. Unlike the recent literature on this subject, here no restrictions are required about the monotonicity and concavity of the incidence rate with respect to the infectious class. Among the applications, the noteworthy case of a convex incidence rate is provided.