Studies On Dynamics Of Virus Infection

The aim of this work is to construct several viral infection models within-host and to analyze the dynamic behavior of these models. In the first part, we investigate the global stability of a viral infection model with lytic and (or) nonlytic immune responses and the sufficient conditions for the global stability of the disease-free steady state and the disease steady state arc obtained. Especially, when the efficacy of the lytic component is neglected, using a geometrical approach, we obtain a different type of conditions for the global stability of the disease steady state. Note that the basic reproduction ratio (BRR) of virus is independent of the parameters related to the immune system. This is an interesting analytical result with a relevant biological significance: the disease never becomes extinct if the BRR is greater than one, independently of the "promptness" of the immunesystem of the patient, which has action only in reducing the " force of infection".Note that many works on immune circadian rhythms have been done by experimental immunologists for the aspects of immunocyte, immunorcsponsion and immunomodulation. A viral infection model is proposed to describe the periodic lytic immune response in the second part. The threshold value for virus tend to extinction or persistence is gained and the virus load must be fluctuant as soon as it is persistent. Furthermore, using numerical simulations, we find that there are complex dynamics. Under different parameters of the model, period triplication and period doubling bifurcations maybe occur and the period doubling cascade proceeds gradually toward chaotic as the amplitude of lytic component is increased. At the same time, the inverse period doubling can be observed. These results can be used to explain the oscillation behaviors of virus population, which was observed in chronic HBV or HCV carriers.As shown in some reference, antigenic stimulation generating CTLs may need a period of time. Thus, time delays can't be ignored in models for immune response. In the third part, we construct a viral infection model under the assumption that the immune response is retarded. Analytical and numerical results show that the integrative effect of strength of the lytic component, time delay of immune response and birth rate of susceptible host cells is to create rich dynamics, which include the occurrence of stable periodic solutions and chaotic dynamical behavior. The route from periodic oscillations to chaos is also investigated. These results can also be used to explain irregular real time series data of immune state of patients.In the last part, a mathematical model is proposed to simulate the hepatitis B virus (HBV) infection with spatial dependence. The existence of traveling waves is established via the geometric singular perturbation method and the minimal wave speed is also found. Numerical simulations show that the model admits non-monotone traveling profiles. Influences of various parameters on the minimum wave speed are also discussed. Moreover, the clinical implications of the results arc also presented.