Global Dynamics Study Of Several Classes Of Infectious Disease Models With Age-spatial Structure

Human health has always been the focus of the world's attention,and the first factor that endangers human health must be infectious diseases.The purpose of this paper is to establish an appropriate mathematical model to better understand the transmission mechanism of infectious diseases,to discuss the stability of the equilibrium point of the system by qualitative analysis,to study the development trend and transmission law of infectious diseases,and to prevent and control the spread of infectious diseases.The aim of this paper is to study the global dynamics of the age-spatial malaria epidemic model and the susceptibility-vaccine-infectionrecovery epidemic model(SVIR).Both models are firstly transformed into reactiondiffusion equations.Then,by using fixed point problem theory and Picard series iteration theory,it is proved that the solutions of the two models exist globally,and both models have a unique global attractor,which proves the rationality of the two models.In the case of spatial homogeneity,an explicit expression for the control of disease and the persistence of the basic reproductive number is established.Then,by studying the distribution of characteristic roots of the characteristic equations and constructing appropriate Lyapunov functions,the local stability and global stability of their equilibria are obtained.