A mathematical model for the therapy of the HIV infection

In [17] it was introduced a model to describe the dynamics of the HIV infection when thepatient is under chemotherapy (either RTI or PI). The main idea in [17] was to introduce theeffectiveness of the drug as a dynamical variable.In this paper we pursue this idea starting from an analysis of the fitness of the virus duringthe therapy. We introduce an adaptive model in which the ability of the viruses to infectthe target cells is related to the number of contacts between viruses and T–cells that havebeen inhibited by the drug. This approach is similar to the model proposed in [10] for apredator-prey system. However the biological interpretation is different here because in ourcontext the adaptation of the virus is due to the development of resistant virus strains. Weanalyze different combination therapies with three antiviral drugs, which consist of reversetranscriptase inhibitor (RTI) and protease inhibitor (PI) and we show the possibility of verylong latency periods, during which the viral load goes below the detectable level. Theseperiods are followed by a rebound followed by the re–establishing of the conditions previousto the therapy. This dynamics is in good qualitative agreement with the available clinicaldata.