Estimating Domains Of Attraction Of Two Classes Of Infectious Disease Models

Infectious disease dynamics is a theoretical quantitative research on infectious disease of epidemic law,the mathematical model reflects the dynamics of infectious disease.Domain of attraction epidemic model is estimated to be an important issue in the kinetic theory of infectious disease.Domain of attraction,people will predict disease trends and disease prevention provide an important basis for research and guidance systems.Therefore,we need to conduct in-depth study of the domain of attraction epidemic model.In this paper,we study two classes of nonlinear autonomous epidemic models that are with constant input,bilineanity contact rate.One is SIQR epidemic model,the other is SEIR epidemic model.Analyzing the stability of the equilibrium point of the two models,based on moment theory to solve the attraction domain of the system.The main work of this paper includes the following aspects:1.Discussing a class of SIQR epidemic model that is with a constant input and the isolation term.The asymptotic stability of endemic disease's balance points and disease-free balance points are also proved by the Routh Hurwitz criterion.2.The domain of attraction of the system is gained by using the LMI(linear matrix inequality)optimization algorithm based on the theory of moment.3.Discussing a class of SEIR epidemic model that is with a constant input and the population density dependent.The asymptotic stability of endemic disease's balance points and disease-free balance points are also proved by the Routh Hurwitz criterion.4.The domain of attraction of the system is gained by using the LMI optimization algorithm based on the theory of moment.