Mathematical Modeling and Optimal Control Analysis of Cholera Dynamics with Environmental Reservoir
DOI:
https://doi.org/10.62054/ijdm/0204.03Abstract
The article investigates the dynamics of cholera transmission through the construction and analysis of a deterministic compartmental model. Some of the results obtained from the analysis are the derivation of the basic reproduction number, and the stability analysis of the disease-free and endemic equilibria. The sensitivity analysis shows that the most sensitive parameters is the ingestion rate, recruitment of susceptible. Numerical models reveal a steady increase in both symptomatic and asymptomatic infections and continued high bacterial environmental loads when there is no controlled. In contrast, if awareness, quarantine, and treatment controls are put together, then infection prevalence and environmental contamination are greatly reduced. Treatment has a great expense but results in fast reductions of the infection rate; awareness efforts are the most cost-effective as they promote precautionary measures that can help avoid the infection of cholera. Quarantine reduces secondary transmission, a vital supporting role. Cholera containment and eradication need long-term behavioral, quarantine, and treatments, something that is demonstrated within the integrated control framework.
References
Abdulrahim, A., Ibrahim, M. N., & Gulumbe, B. H. (2024). Cholera emergency in Nigeria: urgent need for better vaccine access and public health action. Bulletin of the National Research Centre/Bulletin of the National Research Center, 48(1). https://doi.org/10.1186/s42269-024-01242-x.
Al-Arydah, M., Mwasa, A., Tchuenche, J. M., & Smith, R. J. (2013). Modeling Cholera Disease with Education and Chlorination. Journal of Biological Systems, 21(04), 1340007. https://doi.org/10.1142/s021833901340007x.
Al-Shanfari, S., Elmojtaba, I. M., Al-Salti, N., & Al-Shandari, F. (2024). Mathematical analysis and optimal control of cholera–malaria co-infection model. Results in Control and Optimization, 14, 100393. https://doi.org/10.1016/j.rico.2024.100393.
Amadi, P., Lawı, G., & Bonyo, J. (2024). A Metapopulation Model for Cholera with Variable Media Efficacy and Imperfect Vaccine. Journal of Mathematical Sciences and Modelling, 7(1), 20-32. https://doi.org/10.33187/jmsm.1289684
Anteneh, L. M., Zanvo, S. D., Traore, K., & Kakaï, R. G. (2025). Modelling the Impact of Vaccination on Cholera Transmission Dynamics under Stratified Populations and Seasonality. Infectious Disease Modelling, 10(4), 1138–1152. https://doi.org/10.1016/j.idm.2025.06.006
Berhe, H. W. (2020). Optimal control strategies and cost-effectiveness analysis applied to real data of cholera outbreak in Ethiopia’s Oromia region. Chaos Solitons & Fractals, 138, 109933. https://doi.org/10.1016/j.chaos.2020.109933.
Cai, L., Tuncer, N., & Martcheva, M. (2017). How does within-host dynamics affect population-level dynamics? insights from an immuno-epidemiological model of malaria. Mathematical Methods in the Applied Sciences, 20:6424–6450
Cui, X., Xue, D., & Pan, F. (2022). A fractional SVIR-B epidemic model for Cholera with imperfect vaccination and saturated treatment. The European Physical Journal Plus, 137(12). https://doi.org/10.1140/epjp/s13360-022-03564-z
Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180, 29e48
Hezam, I. M., Foul, A., & Alrasheedi, A. (2021). A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen. Advances in Difference Equations, 2021(1). https://doi.org/10.1186/s13662-021-03271-6.
King, A. A., Ionides, E. L., Pascual, M., & Bouma, M. J. (2008). Inapparent infections and cholera dynamics. Nature, 454(7206), 877–880. https://doi.org/10.1038/nature07084
Lakshmikantham, V., Leela, S., & Martynyuk, A. A. (2015). Stability analysis of nonlinear systems. In Systems & control. https://doi.org/10.1007/978-3-319-27200-9.
LaSalle, J. P. & Lefschetz, S. (1961). Stability by Lyapunov's Second Method with Applications. New York: Academic Press.
Lemos-Paião, A. P., Silva, C. J., & Torres, D. F. (2016). An epidemic model for cholera with optimal control treatment. Journal of Computational and Applied Mathematics, 318, 168–180. https://doi.org/10.1016/j.cam.2016.11.002
Lenhart, S. and Workman, J.T. (2007) Optimal Control Applied to Biological Models. Mathematical and Computational Biology Series, Chapman & Hall/CRC, London
Maity, B., Banerjee, S., Senapati, A., Pitchford, J., & Chattopadhyay, J. (2025). Coupling plankton and cholera dynamics: Insights into outbreak prediction and practical disease management. PLoS Computational Biology, 21(9), e1013523. https://doi.org/10.1371/journal.pcbi.1013523.
Momoh, A. A., Abdulwasiu, G., Modu, G. U., Onimode, B. M., Ahmed, I., Abubakar, A., & Tariboon, J. (2025). Controlling the Spread of Malaria-Cholera Co-infection with Effective Intervention Strategy. Bangmod International Journal of Mathematical and Computational Science, 11, 75–107. https://doi.org/10.58715/bangmodjmcs.2025.11.5.
Mustapha, U. T., Maigoro, Y. A., Yusuf, A., & Qureshi, S. (2024). Mathematical modeling for the transmission dynamics of cholera with an optimal control strategy. Bulletin of Biomathematics. https://doi.org/10.59292/bulletinbiomath.2024001.
Mukandavire, Z., Liao, S., Wang, J., Gaff, H., Smith, D. L., & Morris, J. G. (2011). Estimating the reproductive numbers for the 2008–2009 cholera outbreaks in Zimbabwe. Proceedings of the National Academy of Sciences, 108(21), 8767–8772. https://doi.org/10.1073/pnas.1019712108.
Nelson, Metet K., Wasike A.M. Adu, Njuguna Edward, & Makwata Harun. (2025). “Mathematical Modelling of Cholera Transmission Dynamics Incorporating Vaccination”. Asian Research Journal of Mathematics 21 (4): 182-95. https://doi.org/10.9734/arjom/2025/v21i4921.
Neilan, R. L. M., Schaefer, E., Gaff, H., Fister, K. R., & Lenhart, S. (2010). Modeling optimal intervention strategies for cholera. Bulletin of Mathematical Biology, 72(8), 2004–2018. https://doi.org/10.1007/s11538-010-9521-8.
Ogunniyi, T.J., Muoneke, A.P., Nimo, F., Yisa, S. S., & Olorunfemi, T. O. (2025). Cholera in Nigeria: a five-decade review of outbreak dynamics and health system responses. J Health Popul Nutr 44, 329. https://doi.org/10.1186/s41043-025-01096-7
Posny, D., Wang, J., Mukandavire, Z., & Modnak, C. (2015). Analyzing transmission dynamics of cholera with public health interventions. Mathematical Biosciences, 264, 38–53. https://doi.org/10.1016/j.mbs.2015.03.006
Sanda, A., Odekunle, M. R., Dione, D., & Momoh, A. A. (2024). Modeling and Stability Analysis of Fractional Human African Trypanosomiasis Dynamics with Optimal Control. Journal of Mathematical Sciences. https://doi.org/10.1007/s10958-024-07413-5
Song, C., Xu, R., Bai, N., Tian, X., & Lin, J. (2020). Global dynamics and optimal control of a cholera transmission model with vaccination strategy and multiple pathways. Mathematical Biosciences & Engineering, 17(4), 4210–4224. https://doi.org/10.3934/mbe.2020233.
Wang J. (2022). Mathematical Models for Cholera Dynamics-A Review. Microorganisms, 10(12), 2358. https://doi.org/10.3390/microorganisms10122358
Wang, X., & Wang, J. (2014). Analysis of cholera epidemics with bacterial growth and spatial movement. Journal of Biological Dynamics, 9(sup1), 233–261. https://doi.org/10.1080/17513758.2014.974696.
WHO (2022). Cholera vaccines: WHO position paper. Weekly Epidemiological Record, 97(25), 317–340.
World Health Organization. (2017). Ending cholera: A global roadmap to 2030. Global Task Force on Cholera Control (GTFCC). World Health Organization. https://www.who.int/publications/i/item/ending-cholera-a-global-roadmap-to-2030.
Yang, C., Wang, X., Gao, D., & Wang, J. (2017). Impact of awareness programs on cholera dynamics: Two modeling approaches. Bulletin of Mathematical Biology, 79(9), 2109–2131. https://doi.org/10.1007/s11538-017-0322-1
Zheng, Q., Luquero, F. J., Ciglenecki, I., Wamala, J. F., Abubakar, A., Welo, P., Hussen, M., Wossen, M., Yennan, S., Keita, A., Lessler, J., Azman, A. S., & Lee, E. C. (2022). Cholera outbreaks in sub-Saharan Africa during 2010-2019: a descriptive analysis. International Journal of Infectious Diseases, 122, 215–221. https://doi.org/10.1016/j.ijid.2022.05.039.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Ayuba Sanda, Mohammed S. Adamu, Abubakar B. Muhammad, Yahaya Ajiya, Alhassan Ibrahim (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors are solely responsible for obtaining permission to reproduce any copyrighted material contained in the manuscript as submitted. Any instance of possible prior publication in any form must be disclosed at the time the manuscript is submitted and a
copy or link to the publication must be provided.
The Journal articles are open access and are distributed under the terms of the Creative
Commons Attribution-NonCommercial-NoDerivs 4.0 IGO License, which permits use,
distribution, and reproduction in any medium, provided the original work is properly cited.
No modifications or commercial use of the articles are permitted.
