Dynamic Analysis Of Reaction-diffusion SVIR Model In A Spatial Heterogeneous Environment

Biomathematics is one of the most popular interdisciplinary subjects.The most active field in the study of biomathematics is population biological system,in which epidemic is an important branch of biomathematics.Epidemiological dynamics is an important method for theoretical quantitative study of epidemics,which has important application value in the prevention and control of epidemics.This paper mainly analyze the space under the heterogeneous environment of SVIR epidemic dynamics properties of the model.1.A reaction-diffusion SVIR epidemic model in a spatial heterogeneous environment is proposed.Firstly,the suitability of the system solution is proved.Then,the basic re?production number R0 is defined and proved to be a threshold parameter that determines the extinction or persistence of the disease.Finally,the global attractivity of the constant positive equilibrium state and the explicit formula of R0 are obtained.2.A reaction-diffusion SVIR model with a fixed latent period and non-local infections is proposed.Firstly,we confirm that the solution of model exists globally and the model has a compact global attractor.Then,the basic reproduction number R0 is derived and proved to be a threshold parameter to predict whether the disease will spread.Finally,the explicit formula of basic reproduction number is obtained when all model parameters to be positive constants and the domain to the one-dimensional case.In addition,we briefly discuss some differences between the models incorporated by standard incidence rate and bilinear incidence rate.