Global Stability For Three Kinds Of Infectious Diseases Models

With the advancement of science and technology and improvement of medicallevel, there are obvious efects for preventing and controlling many infectious dis-eases. But the infectious diseases are still harmful to the human’s health. Recently,more and more scholars research the infectious diseases using diferential equations.In this thesis, we frstly study the local stability and the global stability of a virusdynamics model with double delays. Then, we consider the global stability of anHIV/AIDS epidemic model with diferent latent stages and treatment. At last,an epidemic model with incomplete treatment and vaccination is constructed andanalyzed.In Chapter1, we mainly introduce the background and development situation ofthe subject, and give some theoretical tools and preliminaries serving the discussionin the paper.In Chapter2, we consider the stability of a virus dynamics model with doubledelays. By analyzing the characteristic equations, the local stability of equilibriaof the model is established. By using suitable Lyapunov functionals, the globalstability of equilibria is established. At the same time, some numerical simulationsare given to explain our conclusions.In Chapter3, the global stability of an HIV/AIDS epidemic model with dif-ferent latent stages and treatment is analyzed. We obtain the basic reproductivenumber (0), then we use the comparison theorem to prove the global stabilityof the disease free equilibrium. The globally asymptotically stable of the endemicequilibrium is proved by Lyapunov functional method. At the same time, somenumerical simulations are given to illustrate our analytic results.In Chapter4, an epidemic model with incomplete treatment and vaccination isconstructed. Qualitative analysis of the model about positivity, boundedness, globalstability of the disease free equilibrium and the endemic equilibrium are carried out.Finally, some numerical simulations are given to illustrate our analytic results.