Kinetic Analysis Of The SIRI Infectious Disease Model Based On Recurrent Structure And Spatial Dispersion

In this article,three types of SIRI epidemic models with relapse age applicable to herpes and tuberculosis are studied: reaction-diffusion SIRI model with non-local time delay;reaction-diffusion SIRI model with non-local time lag and periodicity;with Neumann The SIRI model of the spatial structure of the infection age with boundary conditions.Our model takes the form of a spatial non-local reactiondiffusion system,and uses the spectral radius of the regeneration operator to define the basic reproduction number,indicating whether the basic reproduction number is persistent or extinct Threshold parameter.Through the study of the main eigenvalue problem,the threshold dynamics determined by the basic reproduction number is obtained,and the result of disease transmission is discussed.At the same time,the fixed point theorem is used to prove the existence and uniqueness of the bilinear system.And through the analysis of the characteristics and distribution of the characteristic equation and the construction of the Lyapunov function method,the local dynamics and global dynamics of the system at the disease-free equilibrium and the positive equilibrium are proved.