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Optimal Control Model for Alcohol–Related Risk Behaviors and Beliefs in Tanzania

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  • Maranya M. Mayengo

Abstract

An optimal control theory is applied to a system of ordinary differential equations representing the dynamics of health‐related risks associated with alcoholism in the community with active religious beliefs. Two nonautonomous control variables are proposed to reduce the health risks associated with alcoholism in the community. Consequently, three control strategies are presented using Pontryagin’s maximum principle (PMP), and the necessary conditions for the existence of the optimal controls are obtained. The simulation results revealed that the health risks associated with alcoholism behaviors may be effectively eradicated when both controls, u1(t) and u2(t), are applied in a combination. On the other hand, the cost–effective analysis of the three different strategies confirmed that the desired cost–effective results may be attained when both controls, u1(t) and u2(t), are applied together. Based on these results, this study concludes that, health risks associated with alcoholism behaviors may be efficiently and cost–effectively eradicated from the community when both controls, u1(t) and u2(t), are applied together. Whereas application of control option u1(t) implies increasing the level of protection to the susceptible population by implementing public health education campaign; the control option u2(t) implies increasing the removal rate of the moderate risky individuals into recovered population. The control strategy in which the two options are featured in a combination is presented in this study as Strategy C exhibiting the least ICER value and more cost–effective than the rest of strategies presented.

Suggested Citation

  • Maranya M. Mayengo, 2022. "Optimal Control Model for Alcohol–Related Risk Behaviors and Beliefs in Tanzania," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnljam:v:2022:y:2022:i:1:n:9094494
    DOI: 10.1155/2022/9094494
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    References listed on IDEAS

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    1. Maranya M. Mayengo & Moatlhodi Kgosimore & Snehashish Chakraverty, 2020. "Fuzzy Modeling for the Dynamics of Alcohol‐Related Health Risks with Changing Behaviors via Cultural Beliefs," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    2. Nkuba Nyerere & Livingstone S. Luboobi & Saul C. Mpeshe & Gabriel M. Shirima, 2020. "Optimal Control Strategies for the Infectiology of Brucellosis," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2020, pages 1-17, May.
    3. Xun-Yang Wang & Hai-Feng Huo & Qing-Kai Kong & Wei-Xuan Shi, 2014. "Optimal Control Strategies in an Alcoholism Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Maranya M. Mayengo & Moatlhodi Kgosimore & Snehashish Chakraverty, 2020. "Fuzzy Modeling for the Dynamics of Alcohol-Related Health Risks with Changing Behaviors via Cultural Beliefs," Journal of Applied Mathematics, Hindawi, vol. 2020, pages 1-9, July.
    5. Steady Mushayabasa, 2015. "The Role of Optimal Intervention Strategies on Controlling Excessive Alcohol Drinking and Its Adverse Health Effects," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    6. Khajanchi, Subhas & Ghosh, Dibakar, 2015. "The combined effects of optimal control in cancer remission," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 375-388.
    7. Xun-Yang Wang & Hai-Feng Huo & Qing-Kai Kong & Wei-Xuan Shi, 2014. "Optimal Control Strategies in an Alcoholism Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-18, March.
    8. Steady Mushayabasa, 2015. "The Role of Optimal Intervention Strategies on Controlling Excessive Alcohol Drinking and Its Adverse Health Effects," Journal of Applied Mathematics, Hindawi, vol. 2015, pages 1-11, July.
    9. Joel M Francis & Helen A Weiss & Gerry Mshana & Kathy Baisley & Heiner Grosskurth & Saidi H Kapiga, 2015. "The Epidemiology of Alcohol Use and Alcohol Use Disorders among Young People in Northern Tanzania," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-17, October.
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