Comparative study between a deterministic and stochastic model´s for the hematopoietic reconstitution

Abstract

The dynamics of the processes of cell maturation and regeneration is a branch currently in development for medicine, so taking advantage of the facilities of mathematics to model and solve environmental problems, different models of differential equations have been developed to describe these processes. From the existing deterministic models, the particular case of the hematopoietic cell is chosen, for of a comparative study on the influence of the medium on the process of cell maturation. For this, a probabilistic model of differential equations with six compartments is used. The stochastic term or environmental noise in this particular case modeled by a Weiner process. The inclusion of this term makes it possible to perform an analysis conditioned on the influence of the medium of the different processes of cellular maturation, in this case, of the hematopoietic cell. It is established that the stochastic model reflects a more precise approach to the clinical data used.