{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T03:17:45Z","timestamp":1778815065786,"version":"3.51.4"},"reference-count":41,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T00:00:00Z","timestamp":1730073600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>Cholera is a disease of poverty affecting people with inadequate access to safe water and basic sanitation. Conflict, unplanned urbanization and climate change all increase the risk of cholera. In this article, an optimal control deterministic mathematical model of cholera disease with cost-effectiveness analysis is developed and analyzed considering both direct and indirect contact transmission pathways. 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 of 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. Through the implementation of Pontryagin's maximum principle, the characterization of the optimal controls optimality system is established. The numerical simulation results the integrated control strategies 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, it is recommended to the government stakeholders and policymakers to execute any one of the three integrated intervention programs.<\/jats:p>","DOI":"10.3389\/fams.2024.1462701","type":"journal-article","created":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T04:46:23Z","timestamp":1730090783000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Investigation of an optimal control strategy for a cholera disease transmission model with programs"],"prefix":"10.3389","volume":"10","author":[{"given":"Haileyesus Tessema","family":"Alemneh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shewafera Wondimagegnhu","family":"Teklu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Belela Samuel","family":"Kotola","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kassahun Getnet","family":"Mekonen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2024,10,28]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"2314104","DOI":"10.1155\/2022\/2314104","article-title":"Optimal control analysis of treatment strategies of the dynamics of cholera","volume":"2022","author":"Abubakar","year":"2022","journal-title":"J Optimiz"},{"key":"B2","doi-asserted-by":"publisher","first-page":"9353540","DOI":"10.1155\/2023\/9353540","article-title":"Modelling, analysis, and simulation of measles disease transmission dynamics","volume":"2023","author":"Alemneh","year":"2023","journal-title":"Discr Dyn Nat Soc"},{"key":"B3","doi-asserted-by":"crossref","DOI":"10.47974\/JIOS-1271","volume-title":"Modeling, Analyzing and Simulating the Dynamics of Tuberculosis-Covid-19 Co-infection","author":"Alemneh","year":""},{"key":"B4","doi-asserted-by":"publisher","first-page":"360","DOI":"10.3390\/e25020360","article-title":"A well-posed fractional order cholera model with saturated incidence rate","volume":"25","author":"Baba","year":"2023","journal-title":"Entropy"},{"key":"B5","doi-asserted-by":"publisher","first-page":"60","DOI":"10.3390\/axioms10020060","article-title":"Optimal control analysis of cholera dynamics in the presence of asymptotic transmission","volume":"10","author":"Bakare","year":"2021","journal-title":"Axioms"},{"key":"B6","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-007-2247-7","volume-title":"Convexity and Optimization in Banach Spaces.","author":"Barbu","year":"2012"},{"key":"B7","doi-asserted-by":"publisher","first-page":"109933","DOI":"10.1016\/j.chaos.2020.109933","article-title":"Optimal control strategies and cost-effectiveness analysis applied to real data of cholera outbreak in Ethiopia's Oromia region","volume":"138","author":"Berhe","year":"2020","journal-title":"Chaos Solit Fract"},{"key":"B8","doi-asserted-by":"publisher","first-page":"229","DOI":"10.2307\/1403510","article-title":"Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example","volume":"62","author":"Blower","year":"1994","journal-title":"Int Stat Rev"},{"key":"B9","doi-asserted-by":"publisher","first-page":"e15598","DOI":"10.2139\/ssrn.4268747","article-title":"Cholera prevention, control strategies, challenges and World Health Organization initiatives in the Eastern Mediterranean Region: a narrative review","volume":"9","author":"Buliva","year":"2023","journal-title":"Heliyon"},{"key":"B10","doi-asserted-by":"publisher","first-page":"135","DOI":"10.3934\/dcdsb.2004.4.135","article-title":"Optimal control applied to immunotherapy","volume":"4","author":"Burden","year":"2004","journal-title":"Discrete Cont Dyn Syst Ser B"},{"key":"B11","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3667-0","volume-title":"Mathematical Approaches for Emerging and Reemerging Infectious diseases: Models, Methods, and Theory.","author":"Castillo-Chavez","year":"2002"},{"key":"B12","doi-asserted-by":"publisher","first-page":"845057","DOI":"10.3389\/fpubh.2022.845057","article-title":"Inadequate hand washing, lack of clean drinking water and latrines as major determinants of cholera outbreak in Somali region, Ethiopia in 2019","volume":"10","author":"Challa","year":"2022","journal-title":"Front Public Health"},{"key":"B13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.12737\/1855784","article-title":"Fractional derivative and optimal control analysis of cholera epidemic model","volume":"2022","author":"Cheneke","year":"2022","journal-title":"J Math"},{"key":"B14","volume-title":"An Introduction to Ordinary Differential Equations","author":"Coddington","year":"2012"},{"key":"B15","doi-asserted-by":"crossref","DOI":"10.1063\/1.3059875","volume-title":"Theory of Ordinary Differential Equations","author":"Coddington","year":"1956"},{"key":"B16","doi-asserted-by":"publisher","first-page":"963","DOI":"10.4269\/ajtmh.22-0734","article-title":"Food as a driver of a cholera epidemic in Jijiga, Ethiopia\u2014June 2017","volume":"108","author":"Davis","year":"2023","journal-title":"Am J Trop Med Hyg"},{"key":"B17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.12691\/ajams-7-1-1","article-title":"Modeling and analysis of cholera dynamics with vaccination","volume":"7","author":"Ezeagu","year":"2019","journal-title":"Am J Appl Math Stat"},{"key":"B18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-1-4612-6380-7_1","article-title":"Deterministic and stochastic optimal control","volume":"1","author":"Fleming","year":"1976","journal-title":"Appl Math"},{"key":"B19","first-page":"1","article-title":"Optimizing chemotherapy in an HIV model","volume":"1998","author":"Fister","year":"1998","journal-title":"Electron J Differ Eq"},{"key":"B20","doi-asserted-by":"publisher","first-page":"e0008661","DOI":"10.1371\/journal.pntd.0008661","article-title":"Household spraying in cholera outbreaks: insights from three exploratory, mixed-methods field effectiveness evaluations","volume":"14","author":"Gallandat","year":"2020","journal-title":"PLoS Negl Trop Dis"},{"key":"B21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.15212\/ZOONOSES-2023-0027","article-title":"The threat of cholera in Africa","volume":"42","author":"Erkyihun","year":"2023","journal-title":"Zoonoses"},{"key":"B22","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-77647-5","volume-title":"Optimal Control of Nonlinear Processes","author":"Grass","year":"2008"},{"key":"B23","doi-asserted-by":"publisher","first-page":"157","DOI":"10.3390\/fractalfract6030157","article-title":"Stability analysis and optimal control of a fractional cholera epidemic model","volume":"6","author":"He","year":"2022","journal-title":"Fract Fract"},{"key":"B24","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1080\/17513758.2016.1258093","article-title":"Optimal control and cost effectiveness analysis for Newcastle disease eco-epidemiological model in Tanzania","volume":"11","author":"Hugo","year":"2017","journal-title":"J Biol Dyn"},{"key":"B25","doi-asserted-by":"publisher","first-page":"169","DOI":"10.3390\/tropicalmed8030169","article-title":"Global patterns of trends in cholera mortality","volume":"8","author":"Ilic","year":"2023","journal-title":"Trop Med Infect Dis"},{"key":"B26","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1111\/j.1469-0691.2008.02686.x","article-title":"The impact of climate on the disease dynamics of cholera","volume":"15","author":"Koelle","year":"2009","journal-title":"Clin Microbiol Infect"},{"key":"B27","volume-title":"Stability Analysis of Nonlinear Systems.","author":"Lakshmikantham","year":"1989"},{"key":"B28","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.cam.2016.11.002","article-title":"An epidemic model for cholera with optimal control treatment","volume":"318","author":"Lemos-Pai\u00e3o","year":"2017","journal-title":"J Comp Appl Math"},{"key":"B29","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011418","volume-title":"Optimal Control Applied to Biological Models","author":"Lenhart","year":"2007"},{"key":"B30","doi-asserted-by":"publisher","first-page":"898264","DOI":"10.1155\/2015\/898264","article-title":"Modelling optimal control of cholera in communities linked by migration","volume":"2015","author":"Njagarah","year":"2015","journal-title":"Comp Math Methods Med"},{"key":"B31","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1186\/s13104-019-4504-9","article-title":"Modelling cholera transmission dynamics in the presence of limited resources","volume":"12","author":"Nyabadza","year":"2019","journal-title":"BMC Res Notes"},{"key":"B32","first-page":"35","article-title":"Modelling the transmission dynamics of cholera disease with the impact of control strategies in Nigeria","volume":"20","author":"Onitilo","year":"2023","journal-title":"Cankaya Univ J Sci Eng"},{"key":"B33","doi-asserted-by":"crossref","DOI":"10.1007\/b97412","volume-title":"Introduction to Optimization","author":"Pedregal","year":"2004"},{"key":"B34","volume-title":"Mathematical Theory of Optimal Processes","author":"Pontryagin","year":"1987"},{"key":"B35","doi-asserted-by":"publisher","first-page":"261","DOI":"10.3390\/fractalfract5040261","article-title":"Fractional-order modelling and optimal control of cholera transmission","volume":"5","author":"Rosa","year":"2021","journal-title":"Fract Fract."},{"key":"B36","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.cnsns.2016.10.007","article-title":"Transmission dynamics of cholera: Mathematical modeling and control strategies","volume":"45","author":"Sun","year":"2017","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"B37","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1016\/j.amc.2017.07.063","article-title":"Co-dynamics of pneumonia and typhoid fever diseases with cost effective optimal control analysis","volume":"316","author":"Tilahun","year":"2018","journal-title":"Appl Math Comput"},{"key":"B38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13662-020-03130-w","article-title":"Stochastic and deterministic mathematical model of cholera disease dynamics with direct transmission","volume":"2020","author":"Tilahun","year":"2020","journal-title":"Adv Differ Eq"},{"key":"B39","doi-asserted-by":"publisher","first-page":"147","DOI":"10.3390\/tropicalmed6030147","article-title":"A review of the environmental trigger and transmission components for prediction of cholera","volume":"6","author":"Usmani","year":"2021","journal-title":"Trop Med Infect Dis"},{"key":"B40","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","article-title":"Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission","volume":"180","author":"Van den Driessche","year":"2002","journal-title":"Math Biosci"},{"key":"B41","doi-asserted-by":"publisher","first-page":"2358","DOI":"10.3390\/microorganisms10122358","article-title":"Mathematical models for cholera dynamics\u2014a review","volume":"10","author":"Wang","year":"2022","journal-title":"Microorganisms"}],"container-title":["Frontiers in Applied Mathematics and Statistics"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2024.1462701\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,28]],"date-time":"2024-10-28T04:46:29Z","timestamp":1730090789000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2024.1462701\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,28]]},"references-count":41,"alternative-id":["10.3389\/fams.2024.1462701"],"URL":"https:\/\/doi.org\/10.3389\/fams.2024.1462701","relation":{},"ISSN":["2297-4687"],"issn-type":[{"value":"2297-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,28]]},"article-number":"1462701"}}