有治愈的非线性传染力SIS模型渐近性分析

Asymptotically Analysis of the Curability Nonlinear Infectivity Model

运用微分方程稳定性理论,对有治愈的非线性传染力SIS模型平衡点的稳定性给出定性分析。即求得系统的无病平衡点和正平衡点,并利用线性近似理论和Liapunov泛函研究平衡点的局部稳定和全局渐近稳定性。

By using the stability theory of the ordinary differential Equations, the authors have made a qualitative analysis of the equilibrium points,stability of the Curable Nonlinear Infection Model. It's that, we obtain trivial-equilibrium and positive endemic-equilibrium of the models. Using the signal of characteristic roots and Liapunove functional, we also obtain the sufficient conditions for the local asymptotically stability and global asymptotically stability of the equilibrium points.