ItemArticle

Mathematical and computational analysis of a fractional-order drug abuse model with nonlinear incidence and logistic growth

Title
Mathematical and computational analysis of a fractional-order drug abuse model with nonlinear incidence and logistic growth
Creator
Izadi, Mohammad; Veeresha, Pundikala; Adel, Waleed
Description
This paper presents a novel mathematical model for analyzing the dynamics of drug addiction using a fractional-order system based on the LiouvilleCaputo derivative. The proposed model incorporates a nonlinear saturated incidence rate, logistic growth in the addiction compartments, and seven interconnected subpopulations representing different stages of drug use and recovery, including relapse and awareness. We conduct a rigorous mathematical analysis to establish the existence, uniqueness, positivity, and boundedness of solutions, ensuring the epidemiological and physical validity of the model. The basic reproduction number R0 is derived, and the local and global stability of the equilibrium points is analyzed. A major contribution of this work is the application of a new domain decomposition spectral method based on second-kind Dickson polynomials, combined with the quasilinearization technique, to efficiently solve the complex nonlinear system. The convergence of the numerical method is theoretically validated. Numerical simulations are provided to illustrate the model's dynamics and to explore the impact of various parameters and intervention strategies. Compared to existing models, this study offers an improved framework for understanding memory-dependent behavior in addiction dynamics and introduces a computationally efficient approach to solve fractional-order systems with high accuracy. 2025 International Association for Mathematics and Computers in Simulation (IMACS)
Source
Mathematics and Computers in Simulation;Volume;240;pp.451-472
Date
01-01-2026
Publisher
Elsevier B.V.
Subject
Collocation points; Convergent analysis; Dickson polynomials of the second kind; Drug addicted model; LiouvilleCaputo operator; Stability analysis
Coverage
Izadi M., Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran, Mahani Math Center, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran; Veeresha P., Center for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India; Adel W., Laboratoire Interdisciplinaire de l'Universite Francaise d'Egypte (UFEID Lab), Universite Francaise d'Egypte, Cairo, 11837, Egypt, Department of Mathematics and Engineering Physics, Faculty of Engineering, Mansoura University, Mansoura, 35516, Egypt
Rights
Restricted Access; Hardcopy may be available in the library
Relation
ISSN: 3784754; CODEN: MCSID
Format
online
Language
English
Type
Article

Citation

Izadi, Mohammad; Veeresha, Pundikala; Adel, Waleed, “Mathematical and computational analysis of a fractional-order drug abuse model with nonlinear incidence and logistic growth,” CHRIST (Deemed To Be University) Institutional Repository, accessed June 17, 2026, https://archives.christuniversity.in/items/show/22382.

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