Two Kinds Of Dynamical Models About Within-host Chikungunya Virus

In this thesis, based on the pathogenesis and immune response of within-host chikungunya virus and the study of the virus dynamical models, a within-host chikungunya virus infection model with humoral immune response and delays is developed and analyzed. At the same time, a within-host chikungunya virus infection model with saturation incidence and discrete delays is considered. The dynamical properties with their biological meanings of each model are dis-cussed.Basic knowledge about chikungunya virus, progress of the virus dynamical models and some basic theory are introduced in Chapter 1.In Chapter 2, a within-host chikungunya virus infection model with two delays is proposed. The basic reproductive number R0 is formulated. If R0< 1, the infection-free equilibrium is globally asymptotically stable and the disease always dies out. If R0>1, the global stability of the unique infection equilibrium E1 is proved for the case without the time delay of antigenic stimulation, which can change the stability of E1 and lead to the existence of Hopf bifurcation. Furthermore, explicit formulae for determining the direction of Hopf bifurcation and the sta-bility of bifurcating periodic solutions are established. Finally, some numerical simulations are presented to illustrate the results.In Chapter 3, a within-host Chikungunya virus infection model with discrete delays is pro-posed and analyzed. Firstly, the positivity and boundedness of solutions are proved and the basic reproductive number R0 is computed. Secondly, the existence of equilibria is discussed. There always exits a infection-free equilibrium and there is a unique infection equilibrium when R0> 1. Finally, the global stabilities of the infection-free equilibrium and infection equilibrium are obtained by constructing Lyapunov functionals.In the last chapter, the conclusions of this thesis are briefly reviewed. Then the biological and practical meaning for these models are presented. Finally, some shortcomings of this thesis are discussed and some questions for further research are pointed out.