Exact solutions to fractional pharmacokinetic models using multivariate Mittag-Leffler functions. (March 2023) - Morales-Delgado, V.F.; Taneco-Hernández, M.A.; Vargas-De-León, Cruz; Gómez-Aguilar, J.F.
Abstract: The aim of this paper is to provide a mathematical study of the amount of drug administered as a continuous intravenous infusion or oral dose. For this purpose, we consider fractional-order mammillary-type models describing the anomalous dynamics of exchange of concentrations between compartments at, constant input rates, power-law type, and in the form of oral doses at given (discrete) times. We have developed a general analysis strategy for these models, in which we have found closed-form analytical solutions written in terms of the multivariate Mittag-Leffler function. Numerical simulations have been performed using our formulas, with parameters from the literature. Highlights: Mammillary-type models with Caputo fractional derivative are theoretically analyzed. Fractionalized models do not produce incoherent systems that violate mass balance. Via multivariate Mittag-Leffler function we found exact analytical solutions. We found conditions for the drug concentration to reach a stable level (plateau). Solve models with oral and intravenous administration, with multiple administrations.