Targeting Initiation and Early Recovery to Reduce Alcohol Abuse: A Mathematical Modeling Study in Kenya

Alcoholism is characterized as a chronic disease resulting from compulsive and uncontrollable consumption of alcoholic beverages, which leads to addiction and deterioration of both health and social functioning. 12.2% of the Kenyan population engages in alcohol abuse, while 10.4% are affected by alcohol-use disorders, showing the severity of this public health concern. A Susceptible-Experimenting-Moderate-Quitters-Heavy-Treated (SEMQHT) model was constructed to show the transmission dynamics of alcohol addiction through Ordinary Differential Equations (ODEs), which were solved using the fourth-order Runge-Kutta method. Invariant regions, epidemic thresholds, and model equilibria were analyzed, and the stability of these equilibria was examined. The model was further utilized to evaluate the effects of treatment interventions and cessation of alcohol use. The basic reproduction number was calculated using the next-generation matrix approach. Sensitivity analysis was performed employing normalized forward sensitivity techniques. Local stability of the alcohol-free equilibrium was studied using the Gershgorin Circle Theorem, and global stability was established via the Castillo-Chavez approach. The necessary conditions for the existence of an alcohol-endemic equilibrium were derived, and bifurcation analysis was carried out. Numerical analyses were performed in Python. The analyses showed that those measures that targeted initiation rate and early recovery would significantly reduce alcohol abuse more efficiently than those strategies that only targeted dependent users. Such measures limit the inflow to risky drinking and hasten the recovery of those infected.