Stability analysis of fast food consumption dynamics using a fractional-order framework

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 13 آبان 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.95145.1718

نویسندگان

issam sahib^{* 1}؛ mohamed baroudi¹؛ hicham gourram¹؛ bouchaib khajji²؛ abderrahim labzai²؛ mohamed belam¹

¹Laboratory LMACS, Sultan Moulay Slimane University, MATIC Research Team: Applied Mathematics and Information and Communication Technologie, Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco.

²Laboratory of Analysis, Modeling, and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Morocco.

چکیده

In this research, we propose a novel fractional-order model, referred to as \( PLSCQ \), which is designed to capture the dynamics of fast food consumption and its impact on both health and social behavior. The model incorporates the Caputo derivative and classifies individuals into five distinct categories: potential fast food consumers \( P \), moderate consumers \( L \), excessive consumers \( S \), individuals affected by obesity \( C \), and those who have ceased consuming fast food \( Q \). These categories encompass the full range of fast food consumption behaviors, from those who may potentially consume it to those who have experienced its detrimental consequences, such as obesity, cardiovascular diseases, and other social problems associated with unhealthy eating habits.  The study primarily examines the health risks and behavioral issues associated with fast food consumption. We demonstrate the existence of unique, non-negative solutions and compute the basic reproduction number \( R_0 \). Sensitivity analysis highlights the factors that most significantly influence \( R_0 \), while stability analysis reveals that the system is both locally and globally stable at the equilibrium point with no fast food consumption (\( E_0 \)) when \( R_0 \leq 1 \), and stable with ongoing consumption (\( E^* \)) when \( R_0 > 1 \).  Finally, we present numerical simulations to corroborate the theoretical findings, showing how the order of the partial derivative affects the system's dynamics under varying parameter conditions.

کلیدواژه‌ها

Fast Food؛ Fractional-order؛ Mathematical model؛ Characterization؛ Pontryagin’s maximum principle