A delay mathematical model for HIV dynamics in HIV-specific helper cells

Abstract

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period for the interval of time for cells, with contact with the virus, to be infected by the virions, released by them; (2) a virion production period for the virions to be produced and released to the bloodstream from the infected cells. We compute the reproduction number of the model, R 0, and the stability of the disease-free equilibrium. We find that for values of R 0 < 1, the model approaches asymptotically the disease-free equilibrium. We present numerical simulations of this fact. These results suggest that the model is mathematically and epidemiologically well posed.