In human immunodeficiency virus-infected patients, antiretroviral therapy suppresses the viral replication, which is followed in most patients by a restoration of CD4+ T cells pool. For patients who fail to do so, repeated injections of exogenous interleukin 7 (IL7) are experimented. The IL7 is a cytokine that is involved in the T cell homeostasis and the INSPIRE study has shown that injections of IL7 induced a proliferation of CD4+ T cells. Phase I/II INSPIRE 2 and 3 studies have evaluated a protocol in which a first cycle of three IL7 injections is followed by a new cycle at each visit when the patient has less than 550 CD4 cells/muL. Restoration of the CD4 concentration has been demonstrated, but the long-term best adaptive protocol is yet to be determined. A mechanistic model of the evolution of CD4 after IL7 injections has been developed, which is based on a system of ordinary differential equations and includes random effects. Based on the estimation of this model, we use a Bayesian approach to forecast the dynamics of CD4 in new patients. We propose four prediction-based adaptive protocols of injections to minimize the time spent under 500 CD4 cells/muL for each patient, without increasing the number of injections received too much. We show that our protocols significantly reduce the time spent under 500 CD4 over a period of two years, without increasing the number of injections. These protocols have the potential to increase the efficiency of this therapy.