Analysis Of Global Stability For SEIS Epidemic Model With Standard Incidence

Infectious diseases is always harm to people’s health, it’s every popular brings the hugedisaster for human survival and livelihood. Due to the pathogenesis of infectious diseasesand the reason is not the same, so the study of all kinds of infectious diseases has become anurgent need to solve the world’s problems. Qualitative analysis of infectious disease dynamicsmodel is an important method to study infectious diseases, constructing mathematical modelsto describe the spread of infectious diseases and pathogens mechanisms occurring over timeis the main method, and then combined with the corresponding mathematical knowledgeto describe the disease developments qualitatively, in order to seek the best strategy, thusproviding some theoretical basis and the number of basis for the prevention of the disease.In this thesis, classic SEIS epidemic models with constant recruitment, incubation peri-od, disease-induced death and standard incidence rateare studied. Where A, λ, d, γ, ε, α are positive constant numbers, A is denoted by the suscep-tible population in unit time, d is the natural death rate, α is the disease-induced mortalityrate,1/γand1/εare denoted by the average infectious period and average incubation period ofthe disease respectively. N stands for the size of the total population.Global stabilities of disease-free equilibrium and endemic equilibrium are the most im-portant felds in studying the model. With the help of the qualitative theory of ordinarydiferential equation, using the geometric method set forth in [22], we obtain the sufcientconditions for global stabilities of the disease-free equilibrium and endemic equilibrium. Themethod is based on the developments in higher-dimensional generalization of the criterionof Bendixson and Dulac for planar system, and implies the classic result of the Lyapunovsecond method.The thesis is organized as follows. In chapter1, an introduction about the currentresearch status of infectious disease dynamics model is presented.Chapter2gives some basicproperties of equilibrium system model.The chapter3and chapter4is devoted to investigating the global stability of the disease-free equilibrium and endemic equilibrium. The chapter5contains some numerical simulations to illustrate the results above.