Two Types Of SEIR Model With Vertical Infection And Vaccination

The dynamics of infectious diseases is an important method of theoretical quantitative research.Based on the characteristics of population growth,the occurrence and spread of diseases and the development of law in the population,as well as the associated human factors,mathematical models which can reflect the dynamic characteristics of infectious diseases are established.Through the qualitative and quantitative analysis of model dynamical behavior and numerical simulation,the development of the diseases,popular rule,and the cause and key of the epidemic are analyzed.Based on the Hurwitz’s stability criterion,Lyapunov functional method and single-step design theory,the presented thesis mainly discusses two types of SEIR model problem with vertical infection and vaccination,as well as the disease elimination problem.The main contributions are summarized as follows:Firstly,the background and practical significance of infectious diseases are introduced.Then the impact of vertical infection and vaccination on infectious disease models,together with the realistic meaning and necessity of the epidemic models with time delay are expounded.Then a brief introduction of basic knowledge is given as a foundation of the research.Secondly,the SEIR model with vertical infection and vaccination is established and the equilibriums of the system are studied.Then local asymptotical stability and global asymptotic stability of each equilibrium point are discussed.And the elimination of the disease is considered.Numerical simulations using MATLAB are also given to verify the validity of the conclusions.Thirdly,on the basis of above-mentioned epidemic model,the SEIR model with time-delay in latent period is established and the equilibriums of the system are studied.Then global asymptotical stability of the disease free equilibrium point is discussed.And the condition of endemic equilibrium point’s local asymptotical stability is obtained.Besides,some numerical simulations are given to illustrate our analytic results.Finally,we summarize the conclusion of the thesis and propose unresolved issues of it,which needed to do further research and exploration in the future.