Qualitative Properties Of Two Classes Of SEIR Epidemic Models With Psychological Impact And Treatment

The control of epidemic is a hot topic.Whether the epidemic can be effectively controlled affects the speed of social development seriously.Establishing epidemic model and studying its dynamic properties provides theoretical support for epidemic prevention.Group psychological intervention and treatment are effective measures to control the spread of diseases.Therefore,this paper considers the epidemic model with psychological factors and two treatment strategies,and analyzes its dynamic properties.Detailed contents can be expressed as follows:In chapter 1,we expound the reason and significance of the topic selection,narrate the development process of epidemic model,and give a brief overview of the main research direction and contents of this paper.In chapter 2,a class of epidemic model with psychological influence factors and cure rate of Holling ? type is studied.According to the definition of the basic reproduction number and results of Maple,we obtain the expression of basic reproduction number and two equilibrium points with practical significance.Then we use Routh-Hurwitz criterion and the geometric method to study the stability of the equilibrium point.Through the center manifold theorem and the theory of the branch,this article analyzes the forward or backward bifurcation.Then we give the numerical simulation of global stability.In chapter 3,a class of epidemic model with psychological influencing factors and cure rate of Holling ? type is studied.The basic reproduction number and two equilibrium points of the model are calculated by Maple.After obtaining eigenvalues,stability of two equilibrium points are studied with the method of Routh-Hurwitz criterion.By means of the center manifold theorem and bifurcation theory,conditions for the forward or backward bifurcation are obtained,then the global stability of the endemic equilibrium point is numerically simulated.In chapter 4,two models are compared.Through numerical simulation and parameter perturbation analysis,we find that Holling ? type cure rate and psychological influence factors are more effective in controlling disease transmission.At last,we summarize the main contents of future research.