Global stability of the viral dynamics with Crowley-Martin functional response
Bull. Korean Math. Soc. 2011 Vol. 48, No. 3, 555-574
Published online May 1, 2011
Xueyong Zhou and Jingan Cui
Xinyang Normal University, Beijing University of Civil Engineering and Architecture
Abstract : It is well known that the mathematical models provide very important information for the research of human immunodeciency virus type. However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T-cells and the viral particles. In this paper, a differential equation model of HIV infection of CD4$^+$ T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number $R_01$, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if $R_0>1$. Numerical simulations are presented to illustrate the results.
Keywords : HIV infection, permanence, globally asymptotical stability
MSC numbers : 34D20, 92D30
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