一类SIR传染病模型的稳定性分析
Stability of A Class of SIRS Epidemic Model
本篇以非线性发生率为条件，选择在总人口不为常数情况下，研究了一类SIRS传染病模型的解的有界性和平衡点稳定性，包括无病平衡点的稳定性和地方病平衡点的局部稳定性。运用微分动力系统理论知识证明了无病平衡点是稳定结点，鞍点和退化平衡点。并且使用MATLAB给出了系统在两个平衡点的主要相图，从而进一步验证了本篇理论的正确性。
In this paper the dynamics of an SIRS epidemic model are studied. Under the nonlinear incidence condition and without the assumption that the total population is constant, the local stability and boundedness are considered. It has researched the local asymptotic stability at the disease-free equilibrium as well as at the endemic equilibrium. By Dynamic System theory, the disease-free equilibrium can be stable node, saddle, degenerate equilibrium. Finally by using the mathematical software MATLAB, the correctness of the theory is verified.
朱长荣、吴长青
数学基础医学
传染病模型局部稳定性退化平衡点MATLAB
epidemic modellocal stabilitydegenerate equilibriumMATLAB
朱长荣,吴长青.一类SIR传染病模型的稳定性分析[EB/OL].(2017-04-14)[2025-08-02].http://www.paper.edu.cn/releasepaper/content/201704-141.点此复制
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