Competing HIV Strains and Immune System Response

We consider a simple deterministic model which describes an asymmetric competition between an immune system with a specific and powerful response, and a virus with a broad toxicity and fast mutations. Interest in this model relies on the fact that in spite of it simplicity, it reproduces some of the features of the asymptomatic phase of the infection by HIV-1. In particular, there is a domain of parameters in which the dynamics is characterized by the apparition of \blips", associated here to an instability which develops at high virus reproduction rate. Various possible extensions of this simple model are discussed, in particular in view of its applications in the context of HAART therapy.