Analysis Of Virus Dynamical Models With Immune Response

In thesis,mathematical models are developed based on the antiviral immune re-sponse with HIV viral and bacteriophage.The dynamic properties with their bio-logical meanings are studied.Background knowledge about HIV viral and bacterio-phage,progress of antiviral dynamics and some basic theory are introduced in Chapter 1.In Chapter 2,a mathematical model is proposed to investigate the immune effect of CD8+ T cell in cellular immunity under HIV infection.By constructing Lyapunov functions,the global stabilities of uninfected equilibrium and immune equilibrium are obtained.The effect of activation and died rate of CD8+ T cell for HIV infection are also considered.In the section of numerical simulations,more the immune effect of CD8+ T cell are verified.A model based on the effect of bacteria's CRISPR/Cas immune system is developed in Chapter 3.By equilibria analysis and numerical simulations,it is found that the model exhibits the backward bifurcation?transcritical bifurcation and Hopf bifurcation or more complicated dynamical behaviors.By constructing Lyapunov functions and the theory of consistent continuous,the global stabilities of uninfected equilibrium and coexist equilibrium are obtained.Had a deeper study of the correlation among the CRISPR/Cas immune efficiency,the cost of resistance and the mutation rate for model solutions,and the biological significance are explained in the last.