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 mechanism