A mathematical model for the therapy of the HIV infection

In this paper we consider the evolution of the HIV infection under a highly effective treatment based on a combination of RTI and/or PI drugs. This is usually modelled with a set of ODEs where the drug efficacy is a constant. In this paper we consider the treatment efficacy as a dynamic variable which evolves during the treatment. To model the dynamics of the drug efficacy we use an evolutive type assumption. The resulting set of ODEs are able to reproduce the typical pattern of the illness evolution under treatment: a period of remission, which can last several years, followed by a progressive recrudescence and a viral rebound.