Mathematical analysis of the global dynamics of a power law model for HIV infection of CD4+ T cells

Abstract

We analyze a mathematical power law model that describes HIV infection of CD4+ T cells. We report that the number of critical points depends on n , where n is a positive integer. We show that for any positive integer n the infection – free equilibrium is asymptotically stable if the reproduction number R₀ < 1 and unstable if R₀ > 1. The method of proof involves Rene Descartes’ theory of positive solutions. The graph of X(uninfected T cells), T*(infected T cells) and V(HIV virus) against time t shows how the groups- the infected, the susceptible and the virus vary with time for various values of the parameter in the model. The results show that the positive integer has a considerable effect on the variations of the groups with time.

Keywords: CD4+ T cells, critical / equilibrium points, reproduction number, asymptotic stability.