The Global Behavior Analysis Of Two Classes Of Epidemic Models

In recent years,the epidemiological models have been received extensive attention by many scholars.In this paper,based on the mechanism of the spread of infectious diseases and the idea of compartmental modelling,we propose a dynamic model with general nonlinear incidence rate and time-varying impulsive control and a Huanglongbing dynamic model with time delay.The threshold values and dynamic behaviors are studied.The main work of this thesis can be summarized as follows:In the first chapter,we first introduce the biological background of our research work.Then we intro-duce some research results on the epidemic models with pulse vaccination and dynamic models for citrus Huanglongbing.Finally,we give some major and useful relevant knowledge of this paper.In the second chapter,an SIVS dynamic model with general nonlinear incidence rate and time-varying impulsive control is studied.Based on two assumptions on the incidence rates,two threshold values R₁ and R₂are obtained.By using the comparison theorem in impulsive differential equations and some technical analysis method,we prove that disease-free periodic solution is globally attractive when R₁<1;and the disease persists when R₂>1.Finally,numerical simulations are performed to illustrate our analytic results.In the third chapter,we establish a citrus Huanglongbing transmission model with time delay.First,we compute the basic reproductive number R₀ of the model and then show that the disease persists when R₀>1.It is also shown that if R₀<1,Huanglongbing will be extinct provided that the invasion intensity of infected citrus tree and infected psyllid are not strong.Furthermore,we establish a set of sufficient conditions for the global attractivity of the endemic equilibrium by the method of fluctuations.