含有免疫作用的SIR传染病模型的动力学性质分析

Analysis of the dynamic properties of SIR epidemic model with immunity

为预防并控制传染病的传播,在一类复杂情形下带有隔离的SIRS模型基础上,提出了含有免疫作用的SIR传染病模型.根据介值定理和平衡点对应的特征根分析,证明了传染病模型的无病平衡点与地方病平衡点的存在唯一性以及渐近稳定性,通过数值模拟验证了所得结论的准确性.

In order to prevent and control the spread of the epidemic disease,gives an SIR epidemic model with immunity based on a complex case of the SIRS model with isolation.According to the analysis of the characteristic roots of the corresponding equilibrium and the intermediate value theorem,proves that the existence and the uniqueness and the asymptotic stability of the SIR epidemic model of free-disease-equilibrium and endemic equilibrium.In addition,the numberical simulation tests the accuracy of the obtained theorem.