具有标准发生率的SIR模型的研究
首发时间:2018-05-09
摘要:目前仍有许多传染病在危害着人类的健康,因此研究传染病模型的动力学性质是具有实际意义和现实价值的。本文利用微分不等式和比较原理这一完全不同于V函数构造的思想,研究了具有标准发生率单群组SIR模型的动力学性质,得到了模型的基本再生数,分析了无病平衡点的稳定性;得到了地方病平衡点的局部稳定性,利用微分不等式和比较原理在一定的限制条件下得到了地方病平衡点的全局稳定性,同时利用数值模拟说明结论的正确性。
关键词: 应用数学 传染病模型 地方病平衡点 稳定性 基本再生数
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Global Stability of SIR Model with Standard Incidence
Abstract:There are still many infectious diseases that endangering human health, therefore it is of practical significance and realistic value to study the dynamic nature of the model of infectious diseases. This paper, by using differential inequalities and comparison principle which are quite different from Lyapunov function, has studied standard incidence of one group dynamics properties of SIR model. We get the basic reproduction number and the stability of the disease-free equilibrium is analyzed. The local stability of endemic equilibrium is analyzed and with the help of the differential inequalities and the comparison principle, the global stability of the endemic equilibrium is obtained under certain restriction conditions. At the same time, some numerical simulations are given to verify our conclusions.
Keywords: applied mathematics epidemic model endemic equilibrium stability basic reproductive number
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