Strategies for Controlling the Spread of Cholera through Vaccination, Education, and Quarantine; Model Analysis and Simulation
DOI:
10.29303/jm.v7i4.10479Published:
2025-12-14Downloads
Abstract
Cholera is an infectious disease transmitted through water contaminated with Vibrio cholerae bacteria. This disease remains a public health challenge, especially in areas with poor sanitation. This study developed an SVIQR-B mathematical model to analyze the dynamics of cholera spread, taking into account the effects of quarantine, vaccination, and environmental hygiene education. The analysis was conducted on disease-free and endemic equilibrium points using a local stability approach based on the basic reproduction number (R0). The results showed that when R0 < 1 , the disease would disappear from the population, while R0 > 1 indicated the potential for endemicity. Sensitivity analysis and numerical simulation results indicate that an increase in the transmission rate and a decrease in vaccine effectiveness cause an increase in the value, while an increase in vaccination coverage and the effectiveness of education contribute to a decrease in infection rates. These findings emphasize the importance of implementing integrated medical and educational interventions in efforts to control cholera in a sustainable manner.
Keywords:
Basic reproduction number Cholera Education Quarantine VaccinationReferences
Abdul, N. S., Yahya, L., Resmawan, R., & Nuha, A. R. (2022). Dynamic analysis of the mathematical model of the spread of cholera with vaccination strategies. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 16(1), 281–292. https://doi.org/10.30598/barekengvol16iss1pp279-290
Abubakar, S. F., & Ibrahim, M. O. (2022). Optimal control analysis of treatment strategies of the dynamics of cholera. Journal of Optimization, 2022, 1–26. https://doi.org/10.1155/2022/2314104
Albalawi, W., Nisar, K. S., Aslam, A., Ozair, M., Hussain, T., Shoaib, M., & Zahran, H. Y. (2023). Mathematical modelling approach to cholera transmission with vaccination strategy. Alexandria Engineering Journal, 75, 191–207. https://doi.org/10.1016/j.aej.2023.05.053
Assegaf, F., Saragih, R., & Handayani, D. (2020). Adaptive sliding mode control for cholera epidemic model. IFAC-PapersOnLine, 53(2), 16092–16099. https://doi.org/10.1016/j.ifacol.2020.12.428
Buliva, E., Elnossery, S., Okwarah, P., Tayyab, M., Brennan, R., & Abubakar, A. (2023). Cholera prevention, control strategies, challenges and world health organization initiatives in the eastern mediterranean region: a narrative review. Heliyon, 9(5), e15598. https://doi.org/10.1016/j.heliyon.2023.e15598
Clemens, J. D., Nair, G. B., Ahmed, T., Qadri, F., & Holmgren, J. (2017). Cholera. The Lancet, 390(10101), 1539–1549. https://doi.org/10.1016/S0140-6736(17)30559-7
Driessche, P. van den, & Watmough, J. (1945). Further notes on the basic reproduction number. In Mathematical Epidemiology. Springer.
Hartley, D. M., Morris, J. G., & Smith, D. L. (2005). Hyperinfectivity: a critical element in the ability of v. Cholerae to cause epidemics? PLoS Medicine, 3(1), e7. https://doi.org/10.1371/journal.pmed.0030007
Hu, Z., Wang, S., & Nie, L. (2023). Dynamics of a partially degenerate reaction-diffusion cholera model with horizontal transmission and phage-bacteria interaction. Electronic Journal of Differential Equations, 2023, 1–38. https://doi.org/10.58997/ejde.2023.08
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
Ndii, M. Z. (2018). Pemodelan Matematika. Deepublish.
Nuha, A. R., & Resmawan. (2020). Analisis model matematika penyebaran penyakit kolera dengan mempertimbangkan masa inkubasi. JURNAL ILMIAH MATEMATIKA DAN TERAPAN, 17(2), 212–229. https://doi.org/10.22487/2540766X.2020.v17.i2.15200
Nuha, A. R., Resmawan, R., Mahmud, S. L., Asriadi, A., Agung, A., & Chasanah, S. I. U. (2023). Analisis dinamik pada model matematika sveibr dengan kontrol optimal untuk pengendalian penyebaran penyakit kolera. Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi, 11(1), 154–165. https://doi.org/10.34312/euler.v11i1.20611
Rahman, A., & Isnaeni, A. (2025). Environmental sanitation challenges and opportunities in indonesia coastal regions : a review. Journal of Epidemiology and Health Science 2(1), 121–126.
Resmawan, R., Yahya, L., Mahmud, S. L., Nuha, A. R., & Laita, N. H. (2023). Dynamic analysis of the mathematical model for the cholera disease spread involving medication and enviromental sanitation. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 17(1), 0341–0360. https://doi.org/10.30598/barekengvol17iss1pp0341-0360
Seidu, B., Wiah, E. N., & Asamoah, J. K. K. (2023). Optimal strategies for control of cholera in the presence of hyper-infective individuals. Results in Physics, 53, 106968. https://doi.org/10.1016/j.rinp.2023.106968
Tian, X., Xu, R., & Lin, J. (2019). Mathematical analysis of a cholera infection model with vaccination strategy. Applied Mathematics and Computation, 361, 517–535. https://doi.org/10.1016/j.amc.2019.05.055
Unicev Indonesia. (2023). Water, sanitation and hygiene. UNICEF. https://www.unicef.org/indonesia/water-sanitation-and-hygiene
World Health Organization. (2023). Cholera. https://www.who.int/news-room/fact-sheets/detail/cholera#:~:text=During the 19th century%2C cholera,and the Americas in 1991.
Xu, H., Tiffany, A., Luquero, F. J., Kanungo, S., Bwire, G., Qadri, F., Garone, D., Ivers, L. C., Lee, E. C., Malembaka, E. B., Mendiboure, V., Bouhenia, M., Breakwell, L., & Azman, A. S. (2025). Protection from killed whole-cell cholera vaccines: a systematic review and meta-analysis. The Lancet Global Health, 13(7), e1203–e1212. https://doi.org/10.1016/S2214-109X(25)00107-X
Yamazaki, K., & Wang, X. (2016). Global well-posedness and asymptotic behavior of solutions to a reaction-convection-diffusion cholera epidemic model. Discrete and Continuous Dynamical Systems - Series B, 21(4), 1297–1316. https://doi.org/10.3934/dcdsb.2016.21.1297
License
Copyright (c) 2025 Agusyarif Rezka Nuha, La Ode Nashar, Andi Agung, Bertu Rianto Takaendengan, Widyastutifajri Nuha

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.




