一类带有种痘的齐次SIR传染病模型分析

Analysis of a homogeneous SIR epidemic model with vaccination

摘要: 讨论了一类带有种痘的齐次SIR模型,利用齐次系统理论研究了该模型平衡点的稳定性.结果表明:当基本再生数R(ψ)1时,无病平衡点局部渐近稳定;当R(ψ)1时,无病平衡点不稳定,同时得到了地方病平衡点稳定性的充分条件.

Abstract: This paper considers an age-structured homogeneous SIR model with vaccination. The stability of the equilibria for this model is investigated by using the theory of homogeneous dynamics system.The results show that the disease free equilibrium is stable if the threshold parameter is less than 1.If the threshold parameter is more than 1,the disease free equilibrium is unstable.An explicit sufficient condition for the stability of endemic equilibrium is obtained.