In this paper we simulated the process of forming polymers in Hemoglobin S (HbS) by using differential equations. It presents an autonomous model, whose most important result is the reduction of the model in the combined almost-normal form. In the non-autonomous model, apart from combined almost-normal form and other results, it is treated the periodic case in general. It is analyzed the issue of stability from multiplying and characteristic indexes. Finally, generalizes model applying Magnus theory, coming to important results in numerical simulations.

The Professor of the University of the State of Amazonas Antonio Ivan Ruiz Chaveco, PhD in Mathematical Sciences, has more of 40 publications in specialized magazines and a extensive participation in national and international scientific events. It has experience in Differential Equations, Mathematics Teaching and Mathematical Modeling.