Dynamic Behavior Study On Reaction-diffusion Infectious Disease Models

In recent years,due to the huge impact of infectious diseases on human survival and development,domestic and foreign researchers have also paid attention to infectious disease models,including the ordinary differential equation model(ODE)and partial differential equation model(PDE),so it is very necessary to further explore the infectious disease model.This thesis studies two types of reaction-diffusion infectious disease models in a spatially heterogeneous environment.The specific research content is as follows:1.In the case of ignoring host movement,a new type of host-pathogen reaction d-iffusion model with general morbidity is established,and threshold dynamics analysis is performed on it.First,the well-posedness of the model solution is proved(existence,unique-ness,boundedness).Second,proving that R₀ is the threshold that determines the extinction or persistence of the disease.Simultaneously,it is obtained that the disease will be extinct when R₀=1.Finally,in a homogeneous space environment,the three model parameter-s are all constant examples,and the specific formula of R₀is obtained.By constructing the Lyapunov function,discussing the stability problem with a unique positive equilibrium point.The theoretical results obtained above can also be used to explore the impact of spatial heterogeneity on disease dynamics and assess the risk of disease transmission.2.Under the environment where the total population is kept constant,a type of reactive diffusion malaria model is established,and threshold dynamics analysis is performed on it.First,it is proved that the solution of the model exists globally,and the model has a tight global attractor.Secondly,the basic reproduction number R₀ is derived,proving that it is a threshold parameter for predicting whether the disease can spread,and at the same time,when R₀=1,the disease will be extinct.Finally,when all parameters are independent of space,the stability of the unique constant positive equilibrium point is discussed using the fluctuation method.