An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control

¹ Department of Mathematics, Faculty of Science, Chiangmai University Chiangmai, 50200 Thailand
² Department of Mathematics, Faculty of Science, Mahidol University Bangkok, 10400 Thailand
³ Department of Mathematics, Syracuse University, Syracuse, NY 12344, USA

Corresponding author: rujira@chiangmai.ac.th

Abstract

Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data.
We analyze a non-linear model of the human immunodeficiency virus (HIV) infection that considers the interaction between a replicating virus, CD4+ T-cell and the cytotoxic-lymphocytes (CTL).We then investigate the intracellular delay effect on the stability of the endemically infected steady state. Criteria are given to ensure that the infected steady state is asymptotically stable for all delays. Model analysis also allows the prediction of a critical delay below which the effector CTL can play a significant role in the immune control mechanism even when the basic reproduction number is high.