Modeling CD4+ T cells dynamics in HIV-infected patients receiving   repeated cycles of exogenous Interleukin 7
  Combination Antiretroviral Therapy (cART) succeeds to control viral replication in most HIV infected patients. This is normally followed by a reconstitution of the CD4$^+$ T cells pool; however, this does not happen for a substantial proportion of patients. For these patients, an immunotherapy based on injections of Interleukin 7 (IL-7) has been recently proposed as a co-adjutant treatment in the hope of obtaining long-term reconstitution of the T cells pool. Several questions arise as to the long-term efficiency of this treatment and the best protocol to apply.   We develop a model based on a system of ordinary differential equations and a statistical model of variability and measurement. We can estimate key parameters of this model using the data from INSPIRE, INSPIRE 2 $\&$ INSPIRE 3 trials. In all three studies, cycles of three injections have been administered; in the last two studies, for the first time, repeated cycles of exogenous IL-7 have been administered. Our aim was to estimate the possible different effects of successive injections in a cycle, to estimate the effect of repeated cycles and to assess different protocols.   The use of dynamical models together with our complex statistical approach allow us to analyze major biological questions. We found a strong effect of IL-7 injections on the proliferation rate; however, the effect of the third injection of the cycle appears to be much weaker than the first ones. Also, despite a slightly weaker effect of repeated cycles with respect to the initial one, our simulations show the ability of this treatment of maintaining adequate CD4$^+$ T cells count for years. We were also able to compare different protocols, showing that cycles of two injections should be sufficient in most cases. %Finally, we also explore the possibility of adaptive protocols. 
Ana Jarne, Daniel Commenges, M\'elanie Prague, Yves Levy, Rodolphe   Thi\'ebaut
stat.AP