Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects.

We consider an SIR-type model of immunological behaviour for HIV dynamics, including the effects of reverse transcriptase inhibitors and other drugs which prevent cellular infection. We use impulsive differential equations to model drug behaviour. We classify different regimes according to whether the drug efficacy is negligible, intermediate or high. We consider two strains of the virus: a wild-type strain that can be controlled by both intermediate and high drug concentrations, and a mutant strain that can only be controlled by high drug concentrations. Drug regimes may take trajectories through one, two or all three regimes, depending on the dosage and the dosing schedule. We demonstrate that drug resistance arises at both intermediate and high drug levels. At low drug levels resistance does not emerge, but the total T cell count is proven to be significantly lower than in the disease-free state. At intermediate drug levels, drug resistance is guaranteed to emerge. At high drug levels, either the drug-resistant strain will dominate or, in the absence of longer-lived reservoirs of infected cells, both viral sub-populations will be cleared. In the latter case the immune system is maintained by a population of T cells which have absorbed sufficient quantities of the drug to prevent infection by even the drug-resistant strain. We provide estimates of a range of dosages and dosing schedules which would, if physiologically tolerable, theoretically eliminate free virus in this system. Our results predict that to control viral load, decreasing the interval between doses is more effective than increasing the dose.