Dynamical Analysis Of Three Classes Of SIR Epidemic Models With Discontinuous Treatment

Three classes of SIR epidemic models with discontinuous treatment were studied in this paper, which was on the basis of the model of the existing literature, and including two classes described by ordinary differential equation and a class with time-delay. by using the theory of differential inclusions, the theory of generalized Lyapunov, and the LaSalle invariance principle, the models' dynamical properties were researched, the influence of the spreading with discontinuous treatment was discussed, the application of controlling the disease was given. This work consists of four chapters.The first chapter mainly introduces mainly introduces the background and the significance of infection diseases, the progresses in this field as well as preliminary knowledge, and summarized the main work of this paper.A class of epidemic model with a latency was studied in the second chapter,the properties, the basic reproduction,and the equilibriums were given by using the theory of differential inclusions. the sufficient condition of the equilibriums' global asymptotic stability was provided by using the theory of generalized Lyapunov,and the LaSalle invariance principle; finally, the noninfected equilibrium's limitedtime property was investigated, the time which the model reach and stay was also listed.Considering on the prevalence of infectious disease, a class of model without permanent immunity was studied in the third chapter, whose structure is similar to the second chapter.A class of delay differential model was researched in the fourth chapter, which was based on the generalized function of the prevalence. After the basic reproduction and equilibrium were found, the equilibrium's global asymptotic stability was provided when R0< 1, by using the theorem of Local Stability and Global Attraction; after the existence and uniqueness theorem of the infected equilibrium were found, global asymptotic stability was proved when R0> 1, by applying the Lyapunov function and the generalized LaSalle invariance principle.