Mathematical Model of HIV superinfection dynamics and R5 to X4 switch
  During the HIV infection several quasispecies of the virus arise, which are able to use different coreceptors, in particular the CCR5 and CXCR4 coreceptors (R5 and X4 phenotypes, respectively). The switch in coreceptor usage has been correlated with a faster progression of the disease to the AIDS phase. As several pharmaceutical companies are starting large phase III trials for R5 and X4 drugs, models are needed to predict the co-evolutionary and competitive dynamics of virus strains. We present a model of HIV early infection which describes the dynamics of R5 quasispecies and a model of HIV late infection which describes the R5 to X4 switch. We report the following findings: after superinfection or coinfection, quasispecies dynamics has time scales of several months and becomes even slower at low number of CD4+ T cells. The curve of CD4+ T cells decreases, during AIDS late stage, and can be described taking into account the X4 related Tumor Necrosis Factor dynamics. Phylogenetic inference of chemokine receptors suggests that viral mutational pathway may generate R5 variants able to interact with chemokine receptors different from CXCR4. This may explain the massive signaling disruptions in the immune system observed during AIDS late stages and may have relevance for vaccination and therapy. 
Luca Sguanci, Franco Bagnoli, Pietro Lio