A Delay Differential Equation Model of HIV Infection, with Therapy and CTL Response

Abstract

In this work we investigate a new mathematical model that describes the interactions between CD4+ T cells, human immunodeficiency virus (HIV), immune response and therapy with two drugs. Also an intracellular delay is incorporated into the model to express the lag between the time the virus contacts a target cell and the time the cell becomes actively infected. The model dynamics is completely defined by the basic reproduction number R0 . If R0 ≤ 1 the disease-free equilibrium is globally asymptotically stable, and if R0 > 1, two endemic steady states exist, and their local stability depends on value of R0 . We show that the intracellular delay affects on value of R0 because a larger intracellular delay can reduce the value of R0 to below one. Finally, numerical simulations are presented to illustrate our theoretical results.