一类具有B-D非线性传染率的传染病模型的全局稳定性分析

摘要

The global stability of the SIQ epidemics model with the B-D nonlinear incidence rate is researched.The threshold value R have been obtained and it shows that there is only a dis-easefree equilibrium point when R1 . With the help of Lyapunov function,some results about the global stability of disease free and endemic equilibrium points have been established,which are applicable for non-monotone,non-concave incidence rate.%对一类具有B-D非线性传染率的传染病模型的全局稳定性进行研究。利用分析计算技巧与李雅谱诺夫函数构造，得到阈值R 及无病平衡点和地方病平衡点的存在条件，证明了无病平衡点和地方病平衡点的局部与全局稳定性。结果表明，具有B-D非线性传染率的传染病模型的平衡解局部稳定性与全局稳定性由含模型参数的阀值来决定。