This work proposes an estimation method to obtain the optimal parameter estimates of a mathematical model, from a set of CD4+T values collected in a HIV patient. To this end, the following scheme is adopted: the first step consists in selecting an initial estimate for the model's parameters as that having minimum square error, from a set
of uniform randomly generated candidates. In the second step, the initial solution is refined by an optimization algorithm with constraints and bounds (imposed by physiology), resulting on the optimal estimate. The proposed method is validated through a simulation study and illustrated with an application to a real data set of
CD4+T cells counts for several HIV patients.