Numerical Solution of a Fractional Differential Equation Model of THC and Its Metabolites
Supervisor Name
Mohammad Marabeh
Supervisor Email
mohammad.marabeh@ptuk.edu.ps
University
Palestine Technical University-Kadoorie
Research field
Mathematics
Bio
Mohammad Marabeh is an Associate Professor of Mathematics and the Head of the Applied Mathematics Department at Palestine Technical University-Kadoorie (PTUK), Tulkarem, Palestine. He previously served as the Assistant Dean of the Faculty of Applied Sciences at PTUK from 2022 to 2024. Dr. Marabeh holds a Ph.D. in Mathematics from Middle East Technical University (METU), Turkey, specializing in Functional Analysis, with a perfect GPA of 4.00. His research focuses on convergence in vector lattices, fuzzy Markov chains, fractional differential equations, and topological structures. Dr. Marabeh has extensive teaching experience at PTUK and Bethlehem University, where he has instructed a wide range of undergraduate and graduate courses. Beyond teaching, Dr. Marabeh has played a significant role in academic administration, serving on multiple selection and organizing committees, including those for hiring part-time instructors and coordinating STEM-related events. He has supervised several master's theses and has been an external and internal examiner for various graduate research projects.
Mathematical modeling is a key tool for understanding complex biological and pharmacokinetic systems. In recent research, the pharmacokinetics of delta-9-tetrahydrocannabinol (THC) and its metabolites (THC–OH and THC–COOH) were described using systems of ordinary differential equations (ODEs) [1]. However, ODE-based models depend on current time state and do not account for memory effects, which can lead to inaccuracies in certain applications—particularly in medical and biological contexts where past states influence current behavior. Therefore, fractional differential equations (FDEs) are introduced as a more general framework that extends ODEs and incorporates memory-dependent dynamics [2]. This project aims to develop a fractional differential equation (FDE) model for the pharmacokinetics of THC and its metabolites. The proposed fractional model will be solved numerically using MATLAB and compared with the corresponding ODE-based model in terms of computational efficiency and accuracy. Additionally, A comparison between different numerical methods for solving FDEs and ODEs will be conducted. By establishing a reliable fractional pharmacokinetic model, this study is expected to enhance the understanding of drug dynamics in the human body while reducing experimental costs and safeguarding patient privacy. References [1] Mahahong, Thanachok, and Teerapol Saleewong. 2023. "A Compartment Pharmacokinetics Model of THC and Its Metabolites after Smoking" Engineering Proceedings 55, no. 1: 4. https://doi.org/10.3390/engproc2023055004. [2] Kilbas, Anatoly A., Hari M. Srivastava, and Juan J. Trujillo. 2006. Theory and Applications of Fractional Differential Equations. Elsevier. https://doi.org/10.1016/S0304-0208(06)80001-0.
