@Article{AJIAM-1-20,
author = {Magau , Hangwelani},
title = {Mathematical Insights into Substance Addiction and Abuse Dynamics via Global Nonlocal Operators},
journal = {African Journal for Industrial and Applied Mathematics},
year = {2025},
volume = {1},
number = {1},
pages = {20--46},
abstract = {<p style="text-align: justify;">This paper introduces a novel mathematical model for capturing the
complex dynamics of drug abuse within populations. Departing from conventional
methodologies, the model employs global derivatives to integrate non-local effects,
thereby offering enhanced insight into the spread and evolution of drug abuse. The
stability analysis and numerical simulations conducted in this study reveal critical thresholds and dynamic behaviors that are instrumental in understanding the
persistence and potential escalation of abuse within communities. Numerical simulations also demonstrate the long-term behavior for different orders of $α,$ and the
effects of the function $g(x)$ are presented, further elucidating the intricate interplay of factors that govern the system’s dynamics. These findings not only shed
light on the underlying mechanisms driving the temporal and spatial patterns of
drug abuse but also provide valuable guidance for designing effective intervention
strategies aimed at mitigating its spread. By systematically manipulating key parameters, the model serves as a powerful tool for exploring the driving factors behind drug abuse diffusion and control. The insights gained from this research have
significant implications for public health policy, offering a rigorous mathematical
framework to inform targeted efforts in curbing the epidemic of drug abuse.</p>},
issn = {3105-3289},
doi = {https://doi.org/10.4208/ajiam.2025-0002},
url = {http://global-sci.org/intro/article_detail/ajiam/24220.html}
}