A DELAYED HIV-1 MODEL WITH MULTIPLE TARGET CELLS AND GENERAL NONLINEAR INCIDENCE RATE

Abstract

We investigate a delayed HIV-1 infection model with general nonlinear incidence functions and two classes of target cells: CD4+ T-cells and macrophages. To account for the time lags between viruses' entry into the corresponding two types of target cells and the production of new virus particles, we incorporate four distributed intracellular delays into the model. We show that the basic reproduction number ℜ0 is the sum of the basic reproduction numbers of HIV-1 infection with CD4+ T-cells and that with macrophages; moreover, if ℜ0 is less than or equal to one, then the HIV-1 infection is cleared from the T-cell population and macrophages; whereas if ℜ0 is larger than one, then the viral concentration maintains at some constant level. It is shown, from both our analytic and numeric results, that ignoring the contributions of macrophages to HIV-1 infection and production will underestimate both the risk of HIV-1 infection and the viral load when persisting. This highlights the important effects of multiple target cells on HIV-1 infection.