OPTIMAL CONTROL ON MATHEMATICAL MODEL OF MPOX DISEASE SPREAD
Abstract
The Global emergency related to mpox infection outside endemic areas occurred in 2022. The United States is one of the areas that has been significantly impacted by the mpox virus. To reduce the number of infection cases, it is essential to control the spread of the disease. This can be achieved through optimal control. The intervention provided to combat the dynamic spread of mpox can be represented in the form of a mathematical model. This model comprises the animal population (SEI) and the human population (SEIR). Furthermore, the model that has been formed also divides humans into high-risk and low-risk populations. The classification is based on the risk of complications and death caused by infection. The model will be analyzed in order to ascertain its disease-free and endemic stability. The spread of mpox is then controlled by healthy living behaviors and antiviral administration to reduce the number of infection cases. To this end, numerical simulations were conducted to visualize the spread of mpox with and without the function of control variables so that optimal results were obtained. The results of the numerical simulation demonstrate that a reduction in infection cases by 64.62% can be achieved by implementing an average rate of healthy living behaviors of 93.15% and distributing an average rate of antivirus at 75.11%.
Downloads
References
F. Patauner, R. Gallo, and E. Durante-Mangoni, “Monkeypox infection: An update for the practicing physician,” Eur. J. Intern. Med., vol. 104, no. August, pp. 1–6, 2022, doi: 10.1016/j.ejim.2022.08.022.
T. Z. Song and Y. T. Zheng, “Monkeypox, wild animals, and potential big problem,” Zool. Res., vol. 43, no. 4, pp. 612–614, 2022, doi: 10.24272/j.issn.2095-8137.2022.217.
CDC, “Mpox in Animals and Pets,” CDC, 2024. https://www.cdc.gov/poxvirus/mpox/veterinarian/mpox-in-animals.html (accessed Mar. 28, 2024).
Kemenkes, Pedoman Pencegahan dan Pengendalian Penyakit Monkeypox, vol. 1, no. 1. Jakarta Selatan, 2022. [Online]. Available: https://www.kemkes.go.id/article/view/19093000001/penyakit-jantung-penyebab-kematian-terbanyak-ke-2-di-indonesia.html
WHO, “Mpox (Monkeypox),” WHO, 2023. https://www.who.int/news-room/fact-sheets/detail/monkeypox (accessed Jan. 20, 2024).
S. B. Kim, J. Jung, and K. R. Peck, “Monkeypox: the resurgence of forgotten things,” Epidemiol. Health, vol. 44, pp. 1–13, 2022, doi: 10.4178/epih.e2022082.
U. States et al., “Epidemiologic and Clinical Features of Mpox-Associated Deaths —,” vol. 72, no. 15, pp. 404–410, 2023, [Online]. Available: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10121256/pdf/mm7215a5.pdf
O. J. Peter, F. A. Oguntolu, M. M. Ojo, A. Olayinka Oyeniyi, R. Jan, and I. Khan, “Fractional order mathematical model of monkeypox transmission dynamics,” Phys. Scr., vol. 97, no. 8, p. 84005, 2022, doi: 10.1088/1402-4896/ac7ebc.
W. Adel, A. Elsonbaty, A. Aldurayhim, and A. El-Mesady, “Investigating the dynamics of a novel fractional-order monkeypox epidemic model with optimal control,” Alexandria Eng. J., vol. 73, pp. 519–542, 2023, doi: 10.1016/j.aej.2023.04.051.
A. Khan, Y. Sabbar, and A. Din, “Stochastic modeling of the Monkeypox 2022 epidemic with cross-infection hypothesis in a highly disturbed environment,” Math. Biosci. Eng., vol. 19, no. 12, pp. 13560–13581, 2022, doi: 10.3934/mbe.2022633.
P. Kumar, M. Vellappandi, Z. A. Khan, S. S M, A. Kaziboni, and V. Govindaraj, “A case study of monkeypox disease in the United States using mathematical modeling with real data,” Math. Comput. Simul., vol. 213, pp. 444–465, 2023, doi: 10.1016/j.matcom.2023.06.016.
J. Gao et al., “Monkeypox outbreaks in the context of the COVID-19 pandemic: Network and clustering analyses of global risks and modified SEIR prediction of epidemic trends,” Front. Public Heal., vol. 11, 2023, doi: 10.3389/fpubh.2023.1052946.
A. M. Alzubaidi, H. A. Othman, S. Ullah, N. Ahmad, and M. M. Alam, “Analysis of Monkeypox viral infection with human to animal transmission via a fractional and Fractal-fractional operators with power law kernel,” Math. Biosci. Eng., vol. 20, no. 4, pp. 6666–6690, 2023, doi: 10.3934/mbe.2023287.
Macrotrends, “U.S. Birth Rate 1950-2024,” Macro, 2023. https://www.macrotrends.net/global-metrics/countries/USA/united-states/birth-rate (accessed Dec. 20, 2023).
Macrotrends, “U.S. Death Rate 1950-2024,” Macrotrends, 2023. https://www.macrotrends.net/global-metrics/countries/USA/united-states/death-rate (accessed Dec. 20, 2023).
W. Sudsutad, C. Thaiprayoon, J. Kongson, and W. Sae-Dan, “A mathematical model for fractal-fractional monkeypox disease and its application to real data,” AIMS Math., vol. 9, no. 4, pp. 8516–8563, 2024, doi: 10.3934/math.2024414.
S. Li, Samreen, S. Ullah, S. A. AlQahtani, S. M. Tag, and A. Akgül, “Mathematical assessment of Monkeypox with asymptomatic infection: Prediction and optimal control analysis with real data application,” Results Phys., vol. 51, no. May, p. 106726, 2023, doi: 10.1016/j.rinp.2023.106726.
S. Musumeci et al., “A Case of Mpox Reinfection,” Clin. Infect. Dis., vol. 77, no. 1, pp. 135–137, 2023, doi: 10.1093/cid/ciad147.
D. Aldila et al., “A tuberculosis epidemic model as a proxy for the assessment of the novel M72/AS01E vaccine,” Commun. Nonlinear Sci. Numer. Simul., vol. 120, p. 107162, 2023, doi: 10.1016/j.cnsns.2023.107162.
H. Sulisti, E. Noviani, and N. Kusumastuti, “Analisis Kestabilan Model Dinamika Penyebaran Penyakit Flu Burung,” Bimaster, vol. 03, no. 3, pp. 235–244, 2014, [Online]. Available: http://download.portalgaruda.org/article.php?article=266336&val=2316&title=ANALISIS KESTABILAN MODEL DINAMIKA PENYEBARAN PENYAKIT FLU BURUNG
L. Budiyarto, A. A. Sabila, and H. C. Putri, “Infeksi Cacar Monyet (Monkeypox),” J. Med. Hutama, vol. 4, no. 02 Januari, pp. 3224–3236, 2023.
C. Vo et al., “Clinical Characteristics and Outcomes of Patients With Mpox Who Received Tecovirimat in a New York City Health System,” Open Forum Infect. Dis., vol. 10, no. 11, pp. 1–8, 2023, doi: 10.1093/ofid/ofad552.
D. S. Naidu, Optimal Control Systems. New York: CRC Press, 2002.
Centers for Disease Control and Prevention, “U.S. Mpox Case Trends Reported to CDC,” CDC, 2023. https://www.cdc.gov/poxvirus/mpox/response/2022/mpx-trends.html
United States Census, “U.S. and World Population Clock,” Census Bureau, 2024. https://www.census.gov/popclock/ (accessed Mar. 30, 2024).
Copyright (c) 2025 Putri Nabila Ikhsani, Tarmizi Usman, Muhammad Ikhwan
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
