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Dynamic Analysis for Several HIV Models with CTL Immune Response

Author: MouKeWei
Tutor: ZhuHuiYan
School: Nanhua University
Course: Applied Mathematics
Keywords: HIV infection Lyapunov function LaSalle's invariance principle Time Delay Stability switch
CLC: O242.1
Type: Master's thesis
Year: 2011
Downloads: 16
Quote: 0
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Abstract


In this thesis, the two major categories of HIV infection model with CTL immune response , consists of four chapters : the first chapter introduces the background , significance and progress of AIDS research , and a brief introduction to the main work of this paper . Chapter 2 introduces the Holling Ⅱ functional response function established model of HIV infection with the immune response , and analyzed the uninfected equilibrium point , the global asymptotic stability of the infection without immune balance point and the infected immune balance point locally asymptotically stable sex . Finally, the numerical simulation . Chapter III , further improvements in the second chapter on the basis of the mathematical model , taking into account the body requires a certain amount of time from acceptance of the antigenic stimulation to the immune cells , and therefore immune Delay introduced , the establishment of HIV infection model with immune Delay analyzed uninfected equilibrium point of the global asymptotic stability , infection without immune and infected immune balance point of local stability of the sufficient condition . The numerical simulation results show that , when the the susceptible cells generated rate value to meet the conditions of existence of the infected immune balance point and below a critical value , the delay on the stability of the equilibrium point has no effect ; greater than the critical value , With the time delay increases the stability of the switch will occur . Chapter IV study a class of target cells , the infected cells and the immune system interaction model , the model is based on the life of free virus Arnaout , relative to infected cells , and the viral load and the amount of infected cells proportional. The article analyzed the virus infection and infection -free immune balance point locally asymptotically stable sufficient condition for the delay and the numerical simulation of the positive equilibrium is stable , but needs further verification .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Mathematical modeling, approximate calculation > Mathematical modeling
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