Study On The Kinetic Model Of Pseudorabies

This article studies the dynamic models of two types of infectious diseases.One is the ordinary differential equation epidemic model,and the other is the differential-integral epidemic model.This thesis is composed of six chapters.In the first chapter,the background,the research significance and the development of the epidemic models is summarized,the main contents of this paper are also introduced.In the second chapter,the preliminary knowledge and relevant theories about epidemic dynamics models are presented.In the third chapter,we analyze a class of SILR pseudorabies dynamic model with vertical transmission,then we give the basic reproduction numberR₀ and study the global stability of the two equilibria,numerical simulations are also presented.In the fourth chapter,a pseudorabies model with two age structures of adult and juvenile is established.The basic reproduction number of the model is calculated.By the Routh-Hurwitz criteria and Lyapunov function methods,the global stability of the disease-free equilibrium and the positive equilibrium are discussed.In the fifth chapter,a pseudorabies model with infection age is formulated.Based on the linearization method,fluctuation lemma and Lyapunov functionals,local and global stability of the disease-free equilibrium and the positive equilibrium are discussed.In the sixth chapter,this paper summarizes the main research results,and proposes some problems that need to be solved.