Stochastic Modelling of Genotypic Drug-Resistance for Human Immunodeficiency Virus towards Long-Term Combination Therapy

Motivation: Several mathematical models have been investigated for the description of viral dynamics in the human body: HIV-1 infection is a particular and interesting scenario, because the virus attacks cells of the immune system that have a role in the antibody production and its high mutation rate permits to escape both the immune response and, in some cases, the drug pressure. The viral genetic evolution is intrinsically a stochastic process, eventually driven by the drug pressure, dependent on the drug combinations and concentration: in this paper the viral genotypic drug resistance onset is the main focus addressed. The theoretical basis is the modelling of HIV-1 population dynamics as a predator-prey system of differential equations with a time dependent therapy efficacy term, while the viral genome mutation evolution follows a Poisson distribution. The instant probabilities of drug resistance are estimated by means of functions trained from in vitro phenotypes, with a roulette-wheel based mechanisms of resistant selection. Simulations have been designed for treatments made of one and two drugs as well as for combination antiretroviral therapies. The effect of limited adherence to therapy was also analyzed. Sequential treatment change episodes were also exploited with the aim to evaluate optimal synoptic treatment scenarios.Results: The stochastic predator-prey modelling usefully predicted long-term virologic outcomes of evolved HIV-1 strains for selected antiretroviral therapy combinations. For a set of widely used combination therapies, results were consistent with findings reported in literature and with estimates coming from analysis on a large retrospective data base (EuResist)