Distinct effects of protease and reverse transcriptase inhibition in an immunological model of HIV-1 infection with impulsive drug effects

We present an immunological model that considers the dynamics of CD4+ T cells interacting with free virions, reverse transcriptase inhibiting drugs and protease inhibiting drugs. We divide the T cells into multiple classes and use impulsive differential equations to describe the drug activity. As expected, we find that insufficient dosing of either drug corresponds to high viral load and a large population of infectious T cells. The model further predicts that, in the absence of physiological limits on tolerable drug concentrations, sufficiently frequent dosing with the reverse transcriptase inhibitor alone could theoretically maintain the CD4+ T cell count arbitrarily close to the T cell count in the uninfected immune system. However, for frequent dosing of the protease inhibitor alone, the limiting T cell populations may not be enough to maintain the immune system. Furthermore, frequent dosing of both drugs has the same net effect on the T cell population as frequent dosing of the reverse transcriptase inhibitor only. Thus, the two drug classes can have fundamentally different effects on the long-term dynamics and the reverse transcriptase inhibitor, in particular, plays a crucial role in maintaining the immune system. We also provide estimates for the dosing intervals of each drug that could theoretically sustain the T cell population at a desired level.