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ORIGINAL RESEARCH article

Front. Appl. Math. Stat.
Sec. Mathematical Biology
Volume 10 - 2024 | doi: 10.3389/fams.2024.1462701
This article is part of the Research Topic Mathematical Modeling of Diseases at Population-Level and Cellular-Level View all 6 articles

Investigation of an Optimal Control Strategy for a Cholera Diseases Transmission Model with Intervention Programs

Provisionally accepted
Haileyesus T. Alemneh Haileyesus T. Alemneh 1*Shewafera W. Teklu Shewafera W. Teklu 2Belela S. Kotola Belela S. Kotola 3Kassahun G. Mekonen Kassahun G. Mekonen 4
  • 1 College of Natural and Computational Sciences, University of Gondar, Gondar, Ethiopia
  • 2 Debre Berhan University, Debre Berhan, Amhara, Ethiopia
  • 3 College of Natural and Computational Sciences, Oda Bultum University, Chiro, Ethiopia
  • 4 Hawassa University, Awasa, Southern Nations, Nationalities, and Peoples' Region, Ethiopia

The final, formatted version of the article will be published soon.

    In this paper, an optimal control deterministic mathematical model of cholera disease with costeffectiveness analysis is developed and analyzed considering direct and indirect contact transmission pathway. The model qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction number of the model is obtained. We also performed sensitivity analysis on the basic parameters of the model. Then an optimal control problem is designed with a control functional having five controls: vaccination, treatment, environment sanitation and personal hygiene and water quality improvement program. We examined the existence and uniqueness of the optimal controls of the system. Under the implementation of Pontryagin's maximum principle, characterization of the optimal controls optimality system system is established. The numerical simulation results on the integrated control strategies are demonstrated that strategy 2 ,7 and 12 are effective programs to combat cholera disease from the community. Based on the local circumstances, available funds, and resources, government stakeholders and policymakers were advised by the research findings to execute any one of the three integrated intervention programs.

    Keywords: Cholera, Vibro cholerae, stability analysis, optimal control theory, numerical simulation

    Received: 10 Jul 2024; Accepted: 30 Sep 2024.

    Copyright: © 2024 Alemneh, Teklu, Kotola and Mekonen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Haileyesus T. Alemneh, College of Natural and Computational Sciences, University of Gondar, Gondar, Ethiopia

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.