A fractional calculus model for HIV dynamics: real data, parameter estimation and computational strategies

Abstract

This work deals with mathematical modeling applied to the Human Immunodeficiency Virus. Mathematical aspects analysis is presented, discussed and reviewed. A new model based on the Fractional Calculus theory is proposed. Parameter estimations are made via two computational strategies to both classical and fractional models aiming to investigate the effects of Caputo fractional derivative. The real data are from HIV patients undergoing antiretroviral therapy in different immune responses. From a quality analysis proposal based on the intraclass correlation coefficient and mean absolute percentage error, combined with the numerical simulations, it was shown that the adopted methodology is a promising tool in the understanding of the HIV/T-CD4+ interaction.