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Submitted
May 3, 2023
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May 30, 2023
Published
Sep 30, 2023
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Abstract

This paper proposes a mathematical model for cholera using optimal control of treatment through quarantine and water sanitation. Cholera is acute diarrhoea caused by Vibrio cholera bacteria infecting the intestinal tract. The analysis related to the spread of this disease is carried out through a mathematical approach. The constructed mathematical model is demonstrated epidemiologically. The proposed optimal control is the treatment of infected individuals during the quarantine period and sanitation, namely environmental hygiene, especially water. This strategy aims to suppress the number of infected individuals and reduce the concentration of bacteria due to cholera disease. To solve the optimal control problem, we employ the 4th-order forward-backward Runge-Kutta method. Based on the simulation results, the number of individuals infected by cholera and the concentration of bacteria decreased significantly. Moreover, the proposed method can transfer infected to recovered individuals faster than an optimal control treatment.

Keywords

cholera optimal control treatment water sanitation

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

How to Cite
1.
Purnawan H, Aisyatul Faroh R, Hasan Wahyudi M, Cahyaningtias S. Optimal Control with Treatment and Water Sanitation for Cholera Epidemic Model. EKSAKTA [Internet]. 2023Sep.30 [cited 2024Nov.21];23(03):373-81. Available from: https://eksakta.ppj.unp.ac.id/index.php/eksakta/article/view/428

References

  1. Z. Shuai, J. H. Tien, and P. den Driessche. (2012). Cholera models with hyperinfectivity and temporary immunity, Bull. Math. Biol., vol. 74, no. 10, pp. 2423–2445.
  2. A. P. Lemos-Paião, C. J. Silva, and D. F. M. Torres. (2017). An epidemic model for cholera with optimal control treatment, J. Comput. Appl. Math., vol. 318, pp. 168–180.
  3. A. P. Lemos-Paiao, H. Maurer, C. J. Silva, and D. F. M. Torres. (2022). A SIQRB delayed model for cholera and optimal control treatment, Math. Model. Nat. Phenom., vol. 17, p. 25.
  4. A. Mwasa and J. M. Tchuenche. (2011). Mathematical analysis of a cholera model with public health interventions, Biosystems, vol. 105, no. 3, pp. 190–200.
  5. R. L. Miller Neilan, E. Schaefer, H. Gaff, K. R. Fister, and S. Lenhart. (2010). Modeling optimal intervention strategies for cholera, Bull. Math. Biol., vol. 72, pp. 2004–2018.
  6. V. Capasso and S. L. Paveri-Fontana. (2019). A mathematical model for the 1973 cholera epidemic in the European Mediterranean region., Rev. Epidemiol. Sante Publique, vol. 27, no. 2, pp. 121–132.
  7. “Centers for Disease Control and Prevention, Quarantine and Isolation,” 12 May 2023. http://www.cdc.gov/quarantine/historyquarantine.html.
  8. L. Cesari. (2012). Optimization—theory and applications: problems with ordinary differential equations, Springer Science & Business Media, vol.17.
  9. W. H. Fleming and R. W. Rishel. (2012). Deterministic and stochastic optimal control, Springer Science & Business Media, vol.1.
  10. L. S. Pontryagin. (2017). Mathematical theory of optimal processes. CRC press. 1967.
  11. I. Fitria, N. Azahra, C. Agustina, S. Subchan, and S. Cahyaningtias. (2022).Optimal control on cholera disease spreading model with three variables control variation, BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 2, pp. 463–470.
  12. P. Panja. (2019). Optimal control analysis of a cholera epidemic model, Biophys. Rev. Lett., vol. 14, no. 01, pp. 27–48.
  13. S. Rosa and D. F. M. Torres. (2021). Fractional-order modelling and optimal control of cholera transmission, Fractal Fract., vol. 5, no. 4, p. 261.
  14. S. Subchan, S. D. Surjanto, I. Fitria, and D. S. Anggraini. (2020). Optimization of cholera spreading using sanitation, quarantine, education and chlorination control, ICASESS 2019, p. 236.
  15. X. Tian, R. Xu, and J. Lin. (2019). Mathematical analysis of a cholera infection model with vaccination strategy, Appl. Math. Comput., vol. 361, pp. 517–535.
  16. I. Fitria, A. M. Syafi’i, and others. (2019). An epidemic cholera model with control treatment and intervention, Journal of Physics: Conference Series, vol. 1218, no. 1, p. 12046.
  17. H. W. Berhe. (2020). Optimal control strategies and cost-effectiveness analysis applied to real data of cholera outbreak in Ethiopia’s Oromia region, Chaos, Solitons & Fractals, vol. 138, p. 109933.
  18. N. E. Jauhari. (2022). The SEIRS Model Simulation of Cholera Transmission with Treatment and Vaccination, Appl. Math. Comput. Intell., vol. 11, no. 2, pp. 481–491.
  19. E. A. Bakare and S. Hoskova-Mayerova. (2021). Optimal control analysis of cholera dynamics in the presence of asymptotic transmission, Axioms, vol. 10, no. 2, p. 60.
  20. S. F. Abubakar and M. O. Ibrahim. (2022). Optimal Control Analysis of Treatment Strategies of the Dynamics of Cholera, J. Optim., vol. 2022.
  21. X. Zhou, X. Shi, and M. Wei. (2022). Dynamical behavior and optimal control of a stochastic mathematical model for cholera, Chaos, Solitons & Fractals, vol. 156, p. 111854.
  22. J. Yang, C. Modnak, and J. Wang. (2019). Dynamical analysis and optimal control simulation for an age-structured cholera transmission model, J. Franklin Inst., vol. 356, no. 15, pp. 8438.
  23. K. O. Okosun, M. A. Khan, E. Bonyah, and O. O. Okosun. (2019). Cholera-schistosomiasis coinfection dynamics, Optim. Control Appl. Methods, vol. 40, no. 4, pp. 703–727.
  24. D. Posny, J. Wang, Z. Mukandavire, and C. Modnak. (2015). Analyzing transmission dynamics of cholera with public health interventions,Math. Biosci., vol. 264, pp. 38–53.
  25. Z. Mukandavire, S. Liao, J. Wang, H. Gaff, D. L. Smith, and J. G. Morris Jr. (2011). Estimating the reproductive numbers for the 2008--2009 cholera outbreaks in Zimbabwe, Proc. Natl. Acad. Sci., vol. 108, no. 21, pp. 8767–8772.
  26. W. H. Organization. (2011). Global task force on cholera control, cholera country profile: Haiti, 18 May.
  27. D. S. Naidu. (2002). Optimal control systems. CRC press
  28. N. Ilmayasinta and H. Purnawan. (2021). Optimal Control in a Mathematical Model of Smoking., J. Math. & Fundam. Sci., vol. 53, no. 3.
  29. N. Ilmayasinta, E. A. Irhami, and others. (2019). Optimal control for extraction lipid model of microalgae Chlorella Vulgaris using PMP method, Journal of Physics: Conference Series, vol. 1218, no. 1, p. 12043.
  30. S. Lenhart and J. T. Workman. (2007). Optimal control applied to biological models. CRC press.