Malaysian Journal of Mathematical Sciences, September 2026, Vol. 20, No. 3
An Advanced Delay-Based Mathematical Model for Analyzing Campus Drinking Dynamics
Zeb, S., Yatim, S. A. M., Al-Abedi, M. N. B., Arif, I., Kamran, A., and Rafiq, M.
Corresponding Email: shahzeb@student.usm.my, ainor@usm.my
Received date: 30 September 2025
Accepted date: 15 December 2025
Abstract:
For decades, drinking among college students has posed major public health challenges, yet the influence of time delay factors on reducing alcohol use has not been fully examined through mathematical modeling. This study investigates delayed control measures including restricted alcohol access, mandatory interventions, awareness programs, policy enforcement, and non drinking alternatives within a nonlinear delayed NSP model of Non Drinkers, Social Drinkers, and Problem Drinkers. The model analyzes drinking free and endemic equilibrium points and uses basic reproduction numbers to assess stability under different delay conditions. Results show that time delays strongly affect the stability of the drinking free equilibrium, often causing instability and a shift toward persistent alcohol consumption. Graphical findings further illustrate how delays influence transitions between drinking free and endemic states. These results highlight the importance of timely intervention strategies in reducing alcohol abuse on college campuses. The model demonstrates that delaying interventions can worsen alcohol related harm and underscores the need for proactive policies. Sensitivity analysis shows that increased delays reduce the effectiveness of control measures, with greatest impact on the Problem Drinkers group. Numerical simulations reveal that nonstandard finite difference scheme preserves positivity and stability while accurately managing delays, offering insight into effective intervention timing.
Keywords: campus drinking; biological dynamics; drinking habit; delayed model; NSFD.
