An algebraic approach to proving the global stability of a class of epidemic models

作者：Li, Jianquan^*; Xiao, Yanni; Zhang, Fengqin; Yang, Yali

来源：Nonlinear Analysis: Real World Applications , 2012, 13(5): 2006-2016.

DOI：10.1016/j.nonrwa.2011.12.022

• Global stability
• Lyapunov function
• The LaSalle's Invariance Principle

The global stability of an autonomous differential equation system is an important issue for ecological, epidemiological and virus dynamical models. By means of the direct Lyapunov method and the LaSalle's Invariance Principle, an algebraic approach to proving the global stability is presented in this paper. This approach gives a logic and possibly programming method on how to choose coefficients a(i) based on the classic Lyapunov function of the form Sigma(n)(i=1) a(i)(x(i) - x*(i) - x*(i) In x(i)/x*(i)) such that the derivative of the Lyapunov function is negative definite or semidefinite. As an application, the global stability of an SVS-SEIR epidemic model with vaccination and the latent stage is examined. The generality of the approach is also shown by discussing certain cases.

• 出版日期2012-10
• 单位中国人民解放军空军工程大学; 西安交通大学; 运城学院