Dynamics Study Of The Two Types Of Epidemic Models

A class of SIQR epidemic model with discrete time-delay and an HIV-1delayedinfection model with eclipse stage was studied in this paper. Sufficient conditionswhich ensure the globally asymptotically stable for the equilibrium point of the twokinds of models were obtained by constructing Lyapunov functional and using LaSalleinvariable set principle. This work consists of three chapters.The first chapter mainly introduces the background and the significance ofdynamics of infectious diseases as well as progresses in this field，and summarizedthe main work of this paper.Considering on the factors such as isolation of the infected persons andvaccination of the susceptible ones，chapter2analyzed a category of SIQR infectionmodel with delay and vertical transmission. The threshold of the duration anderadication of the disease were obtained in this paper. By analyzing the effect of delayt on the infection dynamics model，sufficient conditions were derived for the diseasefree equilibrium point and endemic equilibrium point with local stability and globalasymptotic stability.An HIV-1delayed dynamic model with eclipse stage was studied and the basicreproductive number R0and the immune response reproductive number wereobtained. When <1, the infection-free equilibrium point is globally asymptoticallystable, when <1<and jjxx> dwx，the infected equilibrium without immuneresponse is globally asymptotically stable; If t=0, when>1and/jx> Sw，theinfected equilibrium with immune response is globally asymptotically stable.