利用代数方法证明地方病平衡点的全局稳定性

Using algebraic method to prove global stability of endemic equilibrium point

利用李雅普诺夫函数和拉萨尔不变性原理,给出了一种证明地方病平衡点的全局稳定性的代数方法.该方法是基于经典李雅普诺夫函数■,研究如何去选择合适的系数a_i,使得经典李雅普诺夫函数的导数是负定的或半负定的.作为一个应用,研究了具有复发的SIRI传染病模型的地方病平衡点的全局稳定性.

By means of the Lyapunov function and the LaSalle’s invariance principle,an algebraic approach to proving the global stability of endemic equilibrium point was presented in this paper.The method was based on the classical Lyapunov function ∑i=1^nai(xi-xi^*-xi^* lnxi/xi^*) and was discussed how to select the appropriate coefficient ai ,such that the derivative of the classical Lyapunov function was negative definite or semidefinite.As an application,the global stability of endemic equilibrium point of SIRI epidemic model with relapse was studied.