Global stability of the viral dynamics with Crowley-Martin functional response

Xueyong Zhou; Jingan Cui

doi:10.4134/BKMS.2011.48.3.555

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(3): 555-574

Printed May 1, 2011

https://doi.org/10.4134/BKMS.2011.48.3.555

Global stability of the viral dynamics with Crowley-Martin functional response

Xueyong Zhou and Jingan Cui

Xinyang Normal University, Beijing University of Civil Engineering and Architecture

Abstract

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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