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.

Alcoholism, Epidemiology, Reproduction number

1. D. Nutt, L. A. King, W. Saulsbury, and C. Blakemore, “Development of a rational scale to assess the harm of drugs of potential misuse,” the Lancet, vol. 369, no. 9566, pp. 1047–1053, 2007. [Google Scholar] [Crossref]

2. M. Schuberth, “The impact of drug trafficking on informal security actors in Kenya,” Africa Spectrum, vol. 49, no. 3, pp. 55–81, 2014. [Google Scholar] [Crossref]

3. K. Mottarella, L. M. Rubin, and T. J. Grites, “The NACADA Journal 2010–2020: A review and future directions,” NACADA Journal, vol. 42, no. 1, pp. 9–21, 2022. [Google Scholar] [Crossref]

4. S. E. Woolf-King and S. A. Maisto, “Alcohol use and high-risk sexual behavior in Sub-Saharan Africa: a narrative review,” Arch. Sex. Behav., vol. 40, no. 1, pp. 17–42, 2011. [Google Scholar] [Crossref]

5. F. Merz, “United Nations Office on Drugs and Crime: World Drug Report 2017. 2017.,” SIRIUS-Zeitschrift für Strategische Analysen, vol. 2, no. 1, pp. 85–86, 2018. [Google Scholar] [Crossref]

6. T. Pankratz, “Understanding Transnational Organised Crime,” Practice (Vol. 2), vol. 41, p. 50, 2012. [Google Scholar] [Crossref]

7. A. Oyefeso, H. Ghodse, C. Clancy, J. Corkery, and R. Goldfinch, “Drug abuse-related mortality: a study of teenage addicts over a 20-year period,” Soc. Psychiatry Psychiatr. Epidemiol., vol. 34, no. 8, pp. 437–441, 1999. [Google Scholar] [Crossref]

8. R. Hornik et al., “Evaluation of the National Youth Anti-Drug Media Campaign: Fourth Semi-Annual Report of Findings, Executive Summary,” Bethesda, MD: National Institute on Drug Abuse Address, 2002. [Google Scholar] [Crossref]

9. B. Kathungu, L. W. Mwaura, and B. Wambugu, “REPORT ON ALCOHOL, DRUGS AND SUBSTANCE ABUSE AMONG PERSONS WITH DISABILITY IN NAIROBI, COAST AND CENTRAL REGIONS KENYA,” 2013, NACADA. [Google Scholar] [Crossref]

10. F. F. Marsiglia et al., “Substance use among adolescents in sub-saharan Africa: A narrative review of epidemiological data,” African Journal of Alcohol and Drug Abuse (AJADA), pp. 81–112, 2024. [Google Scholar] [Crossref]

11. A. Lenhart and M. Madden, “Teens, privacy and online social networks: How teens manage their online identities and personal information in the age of MySpace,” 2007. [Google Scholar] [Crossref]

12. A. K. Misra, A. Sharma, and J. B. Shukla, “Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases,” Math. Comput. Model., vol. 53, no. 5–6, pp. 1221–1228, 2011. [Google Scholar] [Crossref]

13. D. Ariyasinghe et al., “Feasibility and acceptability of an adapted WHO alcohol brief intervention,” 2026. [Google Scholar] [Crossref]

14. P. Boersma, M. A. Villarroel, and A. Vahratian, Heavy drinking among US adults, 2018, vol. 374. US Department of Health and Human Services, Centers for Disease Control and~…, 2020. [Google Scholar] [Crossref]

15. M. K. M. Kamenderi, J. M. J. Muteti, S. K. S. Kimani, and V. O. V. Okioma, “Alcohol use disorders and associated determinants among public sector employees in Kenya,” African Journal of Alcohol and Drug Abuse, vol. 7, no. 2, pp. 3–10, 2022. [Google Scholar] [Crossref]

16. K. Lelei, J. Muteti, A. Njenga, V. Okioma, and K. Lelei, “Policy Brief on The Status of Alcohol And Drug Abuse Control in Kenya for the Period Between 1st January To 30th June 2020,” VOLUME 7: JUNE 2022, p. 66, 2022. [Google Scholar] [Crossref]

17. C. M. Chen and H. Yi, “SURVEILLANCE REPORT# 84 TRENDS IN ALCOHOL-RELATED MORBIDITY AMONG SHORT-STAY COMMUNITY HOSPITAL DISCHARGES, UNITED STATES, 1979–2006,” 2008, National Institute on Alcohol Abuse and Alcoholism, Division of Epidemiology~…. [Google Scholar] [Crossref]

18. C. P. Bhunu, S. Mushayabasa, and others, “Assessing the effects of poverty in tuberculosis transmission dynamics,” Appl. Math. Model., vol. 36, no. 9, pp. 4173–4185, 2012. [Google Scholar] [Crossref]

19. E. White and C. Comiskey, “Heroin epidemics, treatment and ODE modelling,” Math. Biosci., vol. 208, no. 1, pp. 312–324, 2007. [Google Scholar] [Crossref]

20. M. N. Burattini, E. Massad, F. A. B. Coutinho, R. S. de Azevedo-Neto, R. X. Menezes, and L. F. Lopes, “A mathematical model of the impact of crack-cocaine use on the prevalence of HIV/AIDS among drug users,” Math. Comput. Model., vol. 28, no. 3, pp. 21–29, 1998. [Google Scholar] [Crossref]

21. F. Nyabadza, J. B. H. Njagarah, and R. J. Smith, “Modelling the dynamics of crystal meth (‘tik’) abuse in the presence of drug-supply chains in South Africa,” Bull. Math. Biol., vol. 75, no. 1, pp. 24–48, 2013. [Google Scholar] [Crossref]

22. F. M. M. Muli, “Mathematical Analysis of Drugs and Substance Abuse in Kenya among the Adolescents,” Journal of Mathematical Analysis and Modeling, vol. 4, no. 2, pp. 80–100, 2023. [Google Scholar] [Crossref]

23. K. Chinnadurai and S. ATHITHAN, “Mathematical Modelling of The Drinking Behaviour Effect on Society,” Asia Pacific Journal of Mathematics, vol. 10, pp. 10–36, 2023. [Google Scholar] [Crossref]

24. K. Chinnadurai, S. Athithan, and M. G. Kareem, “Mathematical Modelling on Alcohol Consumption Control and its Effect on Poor Population.,” IAENG International Journal of Applied Mathematics, vol. 54, no. 1, 2024. [Google Scholar] [Crossref]

25. M. M. Mayengo, “Modeling the prevalence of alcoholism with compulsory isolation treatment facilities,” Results Phys., vol. 48, p. 106428, 2023. [Google Scholar] [Crossref]

26. F. Nyabadza, “Modeling the effects of treatment on alcohol abuse in Kenya incorporating mass media campaign,” Journal of Mathematical and Computational Science, 2019. [Google Scholar] [Crossref]

27. J. W. Finney and R. H. Moos, “Entering treatment for alcohol abuse: A stress and coping model,” Addiction, vol. 90, no. 9, pp. 1223–1240, 1995. [Google Scholar] [Crossref]

28. P. Renard, A. Alcolea, and D. Ginsbourger, “Stochastic versus deterministic approaches,” Environmental modelling: Finding simplicity in complexity, pp. 133–149, 2013. [Google Scholar] [Crossref]

29. K. P. Slavkova et al., “Mathematical modelling of the dynamics of image-informed tumor habitats in a murine model of glioma,” Sci. Rep., vol. 13, no. 1, p. 2916, 2023. [Google Scholar] [Crossref]

30. T. O. Alade, M. Alnegga, S. Olaniyi, and A. Abidemi, “Mathematical modelling of within-host Chikungunya virus dynamics with adaptive immune response,” Model. Earth Syst. Environ., vol. 9, no. 4, pp. 3837–3849, 2023. [Google Scholar] [Crossref]

31. E. Gayathiri et al., “Computational approaches for modeling and structural design of biological systems: A comprehensive review,” Prog. Biophys. Mol. Biol., vol. 185, pp. 17–32, 2023. [Google Scholar] [Crossref]

32. P. Asplin, M. J. Keeling, R. Mancy, and E. M. Hill, “Epidemiological and health economic implications of symptom propagation in respiratory pathogens: A mathematical modelling investigation,” PLoS Comput. Biol., vol. 20, no. 5, p. e1012096, 2024. [Google Scholar] [Crossref]

33. P. W. Njori, “Mathematical model of sexual orientations in the presence of recovery centers,” International Journal of Statistics and Applied Mathematics, 2025. [Google Scholar] [Crossref]

34. S. Hytner, D. Josselin, D. Belin, and O. Bowden Jones, “Myths and facts about alcohol use disorder: a Delphi consensus study,” Brain Commun., vol. 7, no. 1, p. fcaf035, 2025. [Google Scholar] [Crossref]

35. H. Tilg, S. Petta, N. Stefan, and G. Targher, “Metabolic dysfunction–associated steatotic liver disease in adults: a review,” JAMA, vol. 335, no. 2, pp. 163–174, 2026. [Google Scholar] [Crossref]

36. S. Li, Samreen, S. Ullah, M. B. Riaz, F. A. Awwad, and S. W. Teklu, “Global dynamics and computational modeling approach for analyzing and controlling of alcohol addiction using a novel fractional and fractal–fractional modeling approach,” Sci. Rep., vol. 14, no. 1, p. 5065, 2024. [Google Scholar] [Crossref]

37. A. Vivas, J. Tipton, S. Pant, and A. Fernando, “Mathematical model for the dynamics of alcohol-marijuana co-abuse,” Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 2, pp. 496–516, 2024. [Google Scholar] [Crossref]

38. S. Chege, M. O. Okongo, and J. O. Ochwach, “Mathematical Model of Alcoholism Incorporating Treatment: A Case Study in Kenya,” Journal of Mathematics Instruction, Social Research and Opinion, vol. 4, no. 1, pp. 73–90, 2025. [Google Scholar] [Crossref]

39. I. J. Meem, R. Hossain, and S. A. Samad, “A mathematical model of alcoholism in bangladesh,” Khulna University Studies, pp. 281–290, 2022. [Google Scholar] [Crossref]

40. J. L. Manthey, A. Y. Aidoo, and K. Y. Ward, “Campus drinking: an epidemiological model,” J. Biol. Dyn., vol. 2, no. 3, pp. 346–356, 2008. [Google Scholar] [Crossref]

41. B. Khajji, L. Boujallal, M. Elhia, O. Balatif, and M. Rachik, “A fractional-order model for drinking alcohol behaviour leading to road accidents and violence,” Math. Model. Comput, vol. 9, pp. 501–518, 2022. [Google Scholar] [Crossref]

42. D. R. M. A. LILLESKOV and D. R. C. CHAKUA, “ASSESSMENT OF ALCOHOL AND DRUG USE IN THE PRIVATE SECTOR IN KENYA,” 2013, NACANDA. [Google Scholar] [Crossref]

43. W. H. Organization, Global status report on alcohol and health 2018. World Health Organization, 2018. [Google Scholar] [Crossref]

44. A. C. JUMAI and A. C. AKPAGHER, “USING NONLINEAR MATHEMATICAL MODEL TO STUDY THE IMPACT OF INFECTIOUS DISEASE ON CORONAVIRUS DISEASE IN A FUZZY ENVIRONMENT,” Journal of Systematic and Modern Science Research, 2025. [Google Scholar] [Crossref]

45. H. Cao, D. Yu, and C. L. P. Chen, “Spatiotemporal contagion dynamics driven by human mobility in multilayer activity-driven networks,” Appl. Math. Comput., vol. 522, p. 129993, 2026. [Google Scholar] [Crossref]

46. M. Korkmaz, “Mathematically grounded state of charge estimation via Gershgorin-based feature engineering and ensemble learning from electrochemical impedance spectroscopy data,” Eng. Appl. Artif. Intell., vol. 174, p. 114559, 2026. [Google Scholar] [Crossref]

47. Z. Jin, Y. Yang, J. Yu, B. Wang, S. Cao, and Z. Zhao, “Study on the global stability of members strengthened with outer sleeves,” J. Constr. Steel Res., vol. 239, p. 110250, 2026. [Google Scholar] [Crossref]

48. Z. Faiz, A. S. Ali, A. Thaljaoui, M. A. Badawi, and others, “Modeling and treatment of social media addiction using a fractional-order and deep neural network approach,” Appl. Soft Comput., p. 115440, 2026. [Google Scholar] [Crossref]

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