Global Dynamics And Vaccination Strategy Research For Several Classes Epidemic Models With Latency And Diffusion

This thesis establishes several epidemic models with latency,vaccination and diffusion,further dynamics are mainly studied by means of the basic theories of ordinary differential equation,partial differential equation and delay differential equation,and the methods of a novel geometric criterion of global stability for nonlinear autonomous differential equations,Lyapunov stability theory and La Salle invariance principle,upper and lower solution and Schauder’s fixed point theorem,and so on.The contents are as follows.The first chapter mainly introduces the research background of epidemics,the current research status of epidemic models at home and abroad,and the main work of this paper.In Chapter 2,a nonlinear SEIVS epidemic model with temporary immunity is formulated.By using the next generation matrix,Routh-Hurwitz criterion and the third additive compound matrix,the control reproduction number,the existence and uniqueness,local and global asymptotic stability of the equilibria are obtained.The effective control strategy for hepatitis B is explored by application of optimal control theory.Furthermore,numerical simulations verify the feasibility of the theoretical results.In Chapter 3,a diffusive TB model with early and late latent infections and vaccination is proposed.Firstly,the well-posedness of the solution,the expression of the control reproduction number is computed and the existence and uniqueness,local asymptotic stability of the equilibria are investigated.Next,global threshold dynamics determined by the control reproduction number is proved by constructing Lyapunov function.Finally,the anlytical results are examined by numerical simulations.In Chapter 4,a diffusive SEIVS epidemic model with distributed delays is established to study the well-posedness of the solution and the threshold dynamics of disease extinction or persistence.By constructing suitable upper and lower solutions and Lyapunov functional,incorporating with Schauder fixed point theorem and limit approach,the existence of traveling wave solutions is studied.The nonexistence of traveling wave solutions is also investigated with the help of the theory of asymptotic spreading and the comparison arguments.