The Notion of Stability of a Differential Equation and Delay Differential Equation Model of HIV Infection of CD4+ T-Cells

Abstract

This research presents a deep insight to address the notion of stability of an epidemical model of the HIV infection of CD4+ T-Cells. Initially, the stability of an ordinary differential equation (ODE) model is studied. This is followed by studying a delay differential equation (DDE) model the HIV infection of CD4+ T-Cells. The available literature on the stability analysis of the ODE model and the DDE model of the CD4+ T-Cells shows that the stability of the models depends on the basic reproduction number “R0”. Accordingly, for the basic reproduction number R0 <1, the model is asymptotically stable, whereas, for R0 >1, the models are globally stable. This research further studies the stability of the models and address the lower possible stability limits for the infection rate of CD4+ T-Cells with virus and the reproduction rate of infectious CD4+ T-Cells, respectively. Accordingly, the results shows that the lower possible limits for the infection rate of CD4+ T-Cells with virus are 0.0000027 mm-3 and 0.000066 mm-3 for the ODE and DDE models, respectively. Again, the lower stability limits for the reproduction rate of infectious CD4+ T-Cells with virus are 12 mm3day-1 and 273.4 mm3day-1 for the ODE and DDE models, respectively. The research minutely studies the stability of the models and gives a deep insight of the stability of the ODE and DDE models of the HIV infection of CD4+ T-Cells with virus.