Dynamical Behavior And Optimal Control Of Several Epidemic Models

It is of great significance to study the dynamic behavior and optimal control of epidemic models for human life.The prevention and control strategies for epidemic have increased with the improvement of medical level,which brings new vitality to the research of epidemic.However,compared with a single control strategy,it is obvious that the multiple control strategies are more beneficial to restrain the spread of infectious diseases.At the same time,considering the population mobility,input and output,incidence,media influence,age structure,death due to disease and other practical factors,this paper studies the dynamic behavior and optimal control of the three types of epidemic models with contral strategy.The main contents are as follows:The first chapter is the introduction,which introduces the research background,significance,current situation and main content.The second chapter is preparatory knowledge,which introduces some definitions and theorems in this paper.The third chapter studies the dynamic behavior and optimal control of a class of saturated incidence SVITR epidemic model with vaccination and drug treatment.On the one hand,we obtain the basic reproductive number by using the next generation matrix theory,and provide the existence and stability of disease-free equilibrium and endemic equilibrium by using Hurwitz criterion,Lyapunov function and Lasalle invariable principle;On the other hand,considering the effects of vaccination measures and result and drug therapy on infectious diseases,control variables are introduced,and the expression form of optimal control pair is obtained by using optimal control theory.The fourth chapter studies the dynamic behavior and optimal control of a class of SVEITR epidemic model with media influence,vaccination and drug treatment.Firstly,the dynamic properties of the existence and stability of equilibrium are proved.Then,by introducing control variables into the model,a class of epidemic model with control strategy is established,and the optimal control strategy is analyzed by using Hamiltonian function and Pontryagin maximum principle.The fifth chapter studies the dynamic behavior and optimal control of a bilinear incidence SEIR epidemic model with age structure.We obtain the conditions for the existence of disease-free equilibrium and endemic equilibrium,and the expression of the basic reproduction number.At the same time,considering the different effects of infectious diseases on young and adult individuals,control variables are introduced,the optimal control strategy satisfying the constraint conditions is obtained.