Estimating the dynamics of the drinking epidemic model with control interventions: A sensitivity analysis

Abstract

This article presents a non-linear mathematical model that captures the dynamics of drinking prevalence within a population. The model is analyzed under an optimal control framework, dividing the total population into four compartments: susceptible, heavy drinker, drinker in treatment, and recovered classes. The model’s validity is affirmed through considerations of positivity, boundedness, reproduction number, stability, and sensitivity analysis. Stability theory is employed to explore both local and global stabilities. Sensitivity analysis identifies parameters with a significant impact on the reproduction number (R0{R}_{0}), with maximum sensitivity observed in parameters related to drinking transmission and transitions from heavy drinking to treatment stages. These parameters exhibit sensitivity indices of (0.538,1)\left(0.538,1), indicating that a 10% increase in these parameters would result in a (5.38,1)\left(5.38,1) increase in the threshold quantity. The study introduces an optimal control strategy that involves awareness campaigns and treatment as control variables. These controls aim to minimize the number of heavy drinkers while maximizing the number of recovered individuals. Pontryagin’s maximum principle is used to solve optimal control problems. Additionally, the research explores various parametric settings for each compartment, enriching the study environment. The effectiveness of the proposed control scheme is evaluated through rigorous numerical simulations, highlighting its competitive edge. The results, validated using MATLAB simulations, are detailed throughout the article.

Keywords

• drinking model
• stability
• sensitivity
• optimal control theory
• numerical simulations