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J. Korean Math. Soc. 2005; 42(5): 1071-1086

Printed September 1, 2005

Copyright © The Korean Mathematical Society.

A delay-differential equation model of HIV infection of CD4$^+$ T-cells

Xinyu Song and Shuhan Cheng

Xinyang Normal University, Shandong Agricultural University

Abstract

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In this paper, we introduce a discrete time to the model to describe the time between infection of a CD4$^+$ T-cells, and the emission of viral particles on a cellular level. We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. We also obtain the condition for existence of an orbitally asymptotically stable periodic solution.

Keywords: Hopf bifurcation, Periodic solution, Stability, HIV, HCV

MSC numbers: 34C05, 92D25

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