具有连续预防接种和垂直传染的SIR流行病模型的稳定性分析

The stability analysis of the SIR epidemic models with vertical infection and continuous vaccination

研究一类具有垂直传染和双线性发生率的连续预防接种的SIR模型,得到决定疾病持续生存的阈值。当阈值小于1时,仅存在无病平衡点;当阈值大于1时,除存在无病平衡点外,还存在唯一的地方病平衡点。利用Hurwitz判据得到了地方病平衡点的局部渐近稳定性。利用La-salle不变原理和Liapunov函数得到了无病平衡点和地方病平衡点全局渐近稳定。

An SIR epidemic model with vertical infection, continuous vertical and bilinear incidence rates, is considered. The threshold which determines the existence of the infective disease is found. When it is smaller than 1, there only exists disease free equilibrium;when it is bigger than 1, the endemic equilibrium and the disease free e- quilibrium exist. By Hurwitz criterion, the locally asymptotieal stability of the disease free equilibrium is proved. By Lasalle invariant theorem and Liapunov function, the global asymptotical stability of disease free equilibrium and the endemic equilibrium is proved.