Dynamic Behaviors For Two Classes Of Multi-Patch Epidemic Models

With the outbreak of COVID-19,epidemic models has become one of the hot project once again.Two classes of multi-patch epidemic models are established and related dynamic behaviors are analyzed in this thesis.We hope the conclusions can provide effective suggestions and a reliable theoretical basis to control diseases.This paper consists of two parts.In the first part of this paper,a SEIS multi-patch model is pro-posed and the basic reproductive number is estimated.The effects of population migration rates on the spread of epidemic diseases are given.In this paper,non-negative matrix theory,comparison prin-ciple and uniform persistence theory are used to study the dynamic behaviors of the multi-patch SEIS model.The existence,uniqueness and stability of disease-free equilibrium and uniform persistence of disease are given especially.The matrix theory and stability theory are used to study two classes of two-patch SEIS models.These two models includes no disease death with the same migration rate and only susceptible people migration.In the second part of this paper,the influence of vaccination is considered.In chapter 4,a SEIVS model is proposed.The bifurcation phenomenon of this two-patch SEIVS model is studied by stability theory and bifurcation theory.The local bifurcation conditions for the backward bifurcation are given at the basic reproductive number R₀=1 and the saddle-node bifurcation are studied at the critical value R_c.