Stabilities Analysis Of Some Infectious Models

In this thesis, two mathematical models for CTL immune response andHTLV-I infection of CD4+T-cells are discussed. We consider these two modelsaccording to their different characteristics. One is a virus dynamics model withCTL immune response of an infection rate in general form, the other is anHTLV-I infection model for ATL progression with the cure rate. By analyzingthe basic reproduction numbers, we investigate the dynamics behavior of thesemodels. This thesis consists of three chapters.In the first chapter, related knowledge of epidemic dynamics and progressare introduced. Then we simply introduce the medical knowledge and our mainworks about CTL immune response and HTLV-I infection of CD4+T-cells. Thebasic related mathematical definition and theorems are also introduced.In the second chapter, the virus dynamics model with CTL immuneresponse of an infection rate in general form is formulated and analyzed thestability of equilibirum. If R<0\, the infection-free equilibrium is globallyasymptotically stable and the virus will be cleared. The immune-freeequilibrium is globally asymptotically stable ifi?0>1,/?,<1. Ifi?,>1, the endemicequilibrium persists and is globally stable. In the third chapter, an HTLV-I infection model for ATL progression withthe cure rate is analyzed, the properties of the model are obtained, if R0<1, theinfection-free equilibrium is globally stable; if R()>1,the unique infectedequilibrium is local stable.