GLOBAL STABILITY OF THE VIRAL DYNAMICS WITH CROWLEY-MARTIN FUNCTIONAL RESPONSE

TLDR

Mathematical models of HIV infection are widely used, but most assume a linear infection rate, which reflects a simple interaction between T‑cells and viral particles. In this paper, a differential equation model of HIV infection of CD4⁺ T‑cells with Crowley‑Martin functional response is studied. We prove that if R₀<1 the infection is cleared and the disease dies out, whereas if R₀>1 the infection persists and the chronic steady state is globally asymptotically stable, as illustrated by numerical simulations.

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 <TEX>$CD4^+$</TEX> T-cells with Crowley-Martin function response is studied. We prove that if the basic reproduction number <TEX>$R_0$</TEX> < 1, the HIV infection is cleared from the T-cell population and the disease dies out; if <TEX>$R_0$</TEX> > 1, the HIV infection persists in the host. We find that the chronic disease steady state is globally asymptotically stable if <TEX>$R_0$</TEX> > 1. Numerical simulations are presented to illustrate the results.