具有非线性传染率和连续接种疫苗的SIRS模型分析

Analysis of SIRS Epidemic Model with Nonlinear Incidence Rate and Continuous Vaccination

运用微分动力系统及代数相关理论对一类具有非线性传染率的传染病模型进行分析,得到其基本再生数,并对其无病平衡点和地方病平衡点的存在性和稳定性进行论证,用SIMULINK进行了模型仿真。结果表明:当接种疫苗达到一定比例时,患者数量明显减少,说明接种疫苗对传染病防制有很大作用。

In this paper,a SIRS epidemic model with nonlinear incidence rate and continuous vaccination was discussed.A differential dynamical model of the disease was constructed and analysed by using differential dynamic system and algebra theory.The basic reproduction numbers corresponding to the model was found out,the existence and stability of the disease-free equilibrium and the endemic equilibrium was proved.Finally,numerical simulations of the model were given.The results showed that when vaccination ratio came to a proportion,the number of patients decreased vastly,which means the function of vaccination in epidemic diseases.