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Stability analysis of the immune response and delay virus dynamics model

Author: ZhengZhongWu
Tutor: ZhangFengQin
School: University of North
Course: Applied Mathematics
Keywords: Virus dynamic model Antibody immune CTL immune Time delay Local asymptotical stability Global asymptotical stability Numerical simulations
CLC: O175
Type: Master's thesis
Year: 2010
Downloads: 39
Quote: 0
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Abstract


Viral infection is a process of the interaction of the body with the virus, which invadethe host and reproduce in target organs cell. It will evoke the host body’s immune responsestrategy after the virus invade the host. Antibody immune and CTL immune play animportant role in the immune response. Through the immune response, the virus will bedestroyed or cleared in vivo. Meanwhile, according to the di?erent virus, there exist thedi?erent time delay in the process of the virus invade the host and the host build the immuneresponse. For example, healthy cells is infected by the infected cells, free virus is separatedfrom infected cells, virus is cleared and body’s immune-defense. So considering the immuneresponse and time delay is very necessary in the study of the virus dynamic model. It willcontribute to describe the dynamic characteristic, re?ect the backgrounds of ecology andbiology and explain the practical act of prevention and therapy of virus diseases. Based onthe basic virus dynamic model, this paper mainly discusses the following content:In chapter 2, we build a virus dynamics model with antibody immune response and CTLimmune response respectively. By means of the Lyapunov function, we obtain the globalproperties of infection-free equilibrium, immune-free equilibrium and endemic equilibrium.We find that the infection-free equilibrium is globally asymptotically stable and the viruswill be cleared in vivo when R0≤1, the immune-free equilibrium is globally asymptoticallystable when R0 > 1, R1≤1, the endemic equilibrium is globally asymptotically stable whenR1 > 1.In chapter 3, The stability of a virus dynamic model with di?erent time delay is dis-cussed respectively. First, the time delay of the virus generation and viral clearance isconsidered. Second, a virus dynamic model with nonlinear infection rate and time delay isconsidered. Through the analysis, we obtain the stability of the infection-free equilibriumand the endemic equilibrium. Last the results is validated by the numerical simulations.In chapter 4, we build a virus dynamic model with delay in immune response and discussthe dynamic properties. we obtain the boundedness of solutions, the global properties of infection-free equilibrium and the stability of the endemic equilibrium. Last the numericalsimulations is given.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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