Dynamical Analysis Of Viral Dynamic Models With Immunity Response

In this paper, three viral dynamic models with immunity response are proposed, and the dynamic behaviors as well as the biological meanings of these models are analyzed. There are five chapters.In the first chapter, the background of HIV virus, immunity system and basic content of related mathematical models are introduced.In the second chapter, a HIV dynamical model with helper-independent CTL immune re-sponse is studied. The analysis suggests that the proliferation of active infection cells makes the virus persisting in the host easier. The results show that the virus will be cleared if the basic re-production number R0≤1, and it will persist in the host if R0> 1. Global stability of equilibria is proved by Lyapunov-LaSalle's invariance principle.In the third chapter, the influence of immune impairment on the viral infection is studied. Sufficient conditions for the global asymptotical stability of an immune-free equilibrium and virus-free equilibrium are obtained by Lyapunov-LaSalle's invariance principle. Sufficient con-ditions for the local stability of endemic equilibria are obtained by Routh-Hurwitz criterion. The results suggest that the virus persists in the host if the input rate of susceptible cells is enough large. The results also suggests that there exists a threshold value on the impairment rate if viral infection disrupts the function of antigen. Virus may be controlled by immune system when the impairment rate of HIV doesn't exceed the threshold value. Immune impairment which depends on disrupting function of helper T cells has smaller influence than the immune impairment which depends on disrupting function of antigen.In the fourth chapter, a HIV dynamical model with helper T cells proliferation is studied. Sufficient conditions for the local stability of endemic equilibria are obtained by Routh-Hurwitz criterion. The results suggest that the proliferate ability of helper T cells not only provides more target cells for HIV virus, but also reduces the destructive rate of immune system. The results also suggest that the existence of so-called "Risky threshold" and "Immunodeficiency threshold" on the impairment rate. The former implies that immune system may collapse when the impairment rate of HIV exceeds the threshold value. The latter implies that immune system always collapses when the impairment exceeds the value.In the last chapter, the contents of this paper are summarized. The analytical methods about the dynamic behaviors and the biological meanings of these models are discussed.