Vol. 7 No. 4 (2025): Desember
Open Access
Peer Reviewed

Strategies for Controlling the Spread of Cholera through Vaccination, Education, and Quarantine; Model Analysis and Simulation

Authors

Agusyarif Rezka Nuha , La Ode Nashar , Andi Agung , Bertu Rianto Takaendengan , Widyastutifajri Nuha

DOI:

10.29303/jm.v7i4.10479

Published:

2025-12-14

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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 Vaccination

References

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

Author Biographies

Agusyarif Rezka Nuha, Universitas Negeri Gorontalo

Author Origin : Indonesia

La Ode Nashar, Universitas Negeri Gorontalo

Author Origin : Indonesia

Andi Agung, Universitas Pattimura

Author Origin : Indonesia

Bertu Rianto Takaendengan, Universitas Negeri Gorontalo

Author Origin : Indonesia

Widyastutifajri Nuha, Universitas Pattimura

Author Origin : Indonesia

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How to Cite

Nuha, A. R., Nashar, L. O., Agung, A., Takaendengan, B. R., & Nuha, W. (2025). Strategies for Controlling the Spread of Cholera through Vaccination, Education, and Quarantine; Model Analysis and Simulation. Mandalika Mathematics and Educations Journal, 7(4), 2101–2118. https://doi.org/10.29303/jm.v7i4.10479

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