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

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 aiai based on the classic Lyapunov function of the form ∑i=1nai(xi−xi∗−xi∗lnxi/xi∗) 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.

► An algebraic approach to proving the global stability is presented.
► This approach provides the method of constructing a Lyapunov function and proving the negative definiteness of the derivative.
► An application on an SVS-SEIR epidemic model is examined.
► The generality of the approach is shown.