具有免疫接种且总人口规模变化的SIR传染病模型的稳定性

Stability of an SIR Epidemic Model with Vaccinal Immunity and a Varying Total Population Size

讨论一类具有预防免疫接种且有效接触率依赖于总人口的SIR传染病模型,给出了决定疾病灭绝和持续生存的基本再生数σ的表达式,在一定条件下证明了疾病消除平衡点的全局稳定性,得到了唯一地方病平衡点的存在性和局部渐近稳定性条件.最后研究了具有双线性传染率和标准传染率的两个具体模型,并证明了当σ>1时该模型地方病平衡点的全局渐近稳定性.

The stability of SIR epidemic model with vaccinal immunity and a varying total population size is studied. The basic reproductive number a is found which determines the existence of infective disease. In some conditions, we demonstrate that the disease free equilibrium is globally stable. The existence of a unique endemic equilibrium and the condition of local asymptotic stability are obtained. For the important cases of bilinear and standard incidence of infection, global asymptotic stability of the endemic equilibrium are proved provided the basic reproduction number is more than unity.