一类带隔离项的具非线性传染率的SIQ 模型的全局分析

摘要

The global stability of an isolation SIQ epidemic mode with non-linear incidence rate is studied , and the basic reproduction number R0 was obtained .Based on the Lasalle invariance principle ,the global stability of the disease-free equilibrium was obtained .By means of point theorem and the distribution of equation root ,the existence and uniqueness of endemic equilibrium was obtained ,and the global stability of endemic equilibrium was proved by using theorem of extremal and Lyapunov function .%研究了一类带有隔离项的具有非线性传染率的SIQ传染病模型的全局稳定性。得到了基本再生数 R0，利用L asalle不变集原理，证明了无病平衡点的全局稳定性。利用零点定理及方程根的分布特点。证明了地方病平衡点的存在性及唯一性。同时，借助多元函数微分学关于极值判断定理及Lyapunov函数，证明了地方病平衡点的全局稳定性。