Regina Wahyudyah Sonata Ayu, Hanna Hilyati Aulia


In this paper the number of  humans infected with cholera was controlled under the uncertainty in cholera model parameters. The aim of this research is to design an adaptive control so that the number of infected humans decreases. To achieve this goal, an adaptive controller was proposed to a deterministic model for the transmission of cholera involving five state variables (susceptible humans, infected humans, quarantined humans, recovered humans, and bacterial concentration) and one input control variable, i.e, the proportion of quarantined humans. A control law was designed such that the number of infected humans was decreased tracking the given reference function. The tracking error convergence were analyzed by employing the  Lyapunov theorem. The performance of the proposed controller was evaluated through numerical simulations. The results show that the adaptive controller designed to the model ensures the tracking error convergence such that the number of infected humans has declined.


Adaptive Controller; Cholera; Lyapunov Theorem; Parameter Uncertainty

Full Text:


DOI: https://doi.org/10.15548/mej.v5i2.2546
Abstract views : 134 times
PDF : 58 times


Aghajanzadeh, O., Sharifi, M., Tashakori, S., & Zohoor, H. (2017). Nonlinear adaptive control method for treatment of uncertain hepatitis B virus infection. Biomedical Signal Processing and Control, 38, 174–181.

Ali, M., Nelson, A. R., Lena Lopez, A., & Sack, D. A. (2015). Updated Global Burden of Cholera in Endemic Countries. 9(6). https://doi.org/10.1371/journal.pntd.0003832

Ayu, R. W. S. (2021). Desain kendali adaptif pada model penyebaran demam berdarah dengan melibatkan fase akuatik Nyamuk. 1(1), 1–10. https://ejurnal.unisap.ac.id/index.php/leibniz/article/view/38

Capasso, V., & Paveri-Fontana, S. (1979). A mathematical model for the 1973 cholera epidemic in the European Mediterranean region. Revue d’épidémiologie et de Santé Publique, 27(2), 121–132. https://europepmc.org/article/med/538301

Cui, an, Wu, Z., & Zhou, X. (2014). Mathematical Analysis of a Cholera Model with Vaccination. https://doi.org/10.1155/2014/324767

Lemos-Paião, A. P., Silva, C. J., & Torres, D. F. M. (2017). 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

Moradi, H., Sharifi, M., & Vossoughi, G. (2015). Adaptive robust control of cancer chemotherapy in the presence of parametric uncertainties: A comparison between three hypotheses. Computers in Biology and Medicine, 56, 145–157. https://doi.org/https://doi.org/10.1016/j.compbiomed.2014.11.002

Sharifi, M., & Moradi, H. (2019). Nonlinear composite adaptive control of cancer chemotherapy with online identification of uncertain parameters. Biomedical Signal Processing and Control, 49(360–374). https://doi.org/https://doi.org/10.1016/j.bspc.2018.07.009

Slotine, J.-J. E., & Li, W. (1991). APPLIED NONLINEAR CONTROL.

Torres Codeço, C. (2001). Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir. BMC Infectious Diseases, 1(1), 1. http://www.biomedcentral.com/1471-2334/1/1

WHO. (2019). Cholera Situation in Yemen. May, 22765273. http://www.emro.who.int/images/stories/csr/documents/Cholera_situation_update_Yemen_February_2019.pdf?ua=1


  • There are currently no refbacks.

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

Ruang Jurnal Program Studi Tadris Matematika
Fakultas Tarbiyah dan Keguruan
Universitas Islam Negeri Imam Bojol Padang
email: mej.uinibpadang@gmail.com


Lisensi Creative Commons
Ciptaan disebarluaskan di bawah Lisensi Creative Commons Atribusi-NonKomersial 4.0 Internasional.