Dynamics Analysis On A Two-strain Epidemic Model With Diffusion

The basic goal of infectious disease dynamics was to understand how the interaction between individual and environment affects the transmission process of infectious disease.Considering heterogeneous environment of the reaction-diffusion model provided a good mathematical tool for the study of environmental impact on infectious disease dynamics.This paper aimed to study the evolution of infectious disease of two different strains in heterogeneous environment by establishing the corresponding reaction-diffusion equation model,focusing on the influence of diffusion coefficient on disease transmission in heterogeneous environmentConsidering the free diffusion coefficient of the population,a two-strain reactiondiffusion model was established with stable input term.Firstly,the well-posedness of the model was analyzed through the comparison principle and Hopf Lemma,the basic reproduction numbers of the strain and the number of invasions describing the competitive relationship between the two-strain were obtained.Secondly,Considering that the two boundary equilibrium points could be difficult to verify the classical theory condition of uniform persistence.,in this paper,the two-strain model was simplified to a single strain model.The priori estimates of positive steady-state solution and the semi-trivial steady-state solution are obtained by using the principle of maximum value,and the homotopy invariance of the Leray-Schauder degree was used to verify that the model had a unique semi-trivial steady-state solution.Then,the global stability of the semi-trivial steady-state solution was obtained by using Lyapunov function and La Salle invariance principle,and the asymptotic distribution of the steady-state solution was studied by using Sobolev embedding theorem when the diffusion coefficient tends to 0 or infinity.Finally,the correctness of the theory was verified by numerical simulation.