Discrete Mathematical Model of Fast Food Consumption: Control Approach - Difaa, Youssef; Khajji, Bouchaib; Benaissa, Hicham (Communication in Biomathematical Sciences, 2025)
We investigate a discrete-time model, PLSCQ, to describe interactions among fast food consumer categories, among five population categories: potential consumers (P), moderate consumers (L), excessive consumers (S), obese individuals (C), and individuals who have ceased fast food consumption (Q). We seek for an optimal strategy that minimizes the excessive consumer and obese populations while maximizing the number of individuals who stop or recover. We incorporate three control measures, representing media and education for potential consumers, healthy eating campaigns for excessive consumers, and treatment for obese patients. Employing the discrete-time Pontryagin maximum principle, we derive optimal controls and numerically solve the system in Matlab, verifying the strategy’s effectiveness through simulation results.