Lyapunov Function Construction And Stability Delays Epidemic Model

Dynamics of infectious diseases is one of the important theoretical and quan-titative research methods in studying infectious disease epidemic models. The in-fuence of the spatial heterogeneity of infectious disease transmission and control isone of very important subject in dynamics research. This thesis mainly utilize theframework of global Lyapunov functionals constructed to obtain stability of epidem-ic models with spatial heterogeneity. The research may contribute to enriching theglobal properties in studying dynamics of infectious disease transmission in a certainsense.In this paper, two types of infectious disease models with time-delay: i.e.,the exposed and relapse distribution of multi-group model. The global stabilityis determined by a sharp threshold parameter, called basic reproduction number,when the incidence rate is nonlinear. We focus on how to construct a suitableLyapunov function to solve the problem of global stability of equilibria. Comparingthe deduction and linkness between applying the discretization method and directmethod in constructing Lyapunov functions.On the other hand, one framework of Lyapunov function (functional) method tosolve the problem of the stability of the nonlinear system, provide a series of simpleand efective determined theorems, can play a important role in preventing andcontrol of disease spread, which may provide decision-making basis and theoreticalreference.