Advanced mathematical modeling and prognosication of regulated spatio-temporal dynamics of Monkeypox

Iranian Journal of Numerical Analysis and Optimization

مقاله 11، دوره 14، Issue 4 - شماره پیاپی 31، اسفند 2024، صفحه 1280-1308   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2024.89077.1484

نویسندگان

M. Baroudi^{* 1، 2}؛ I. Smouni^{3، 2}؛ H. Gourram^{4، 2}؛ A. Labzai^{5، 6}؛ M. Belam^{4، 2}

¹Laboratory LMACS, Sultan Moulay Slimane University, MATIC Research Team: Applied Mathematics and Information and Communication Technologie,Polydisciplinary Faculty, Morocco.

²Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco.

³1Laboratory LMACS, Sultan Moulay Slimane University, MATIC Research Team: Applied Mathematics and Information and Communication Technologie

⁴Laboratory LMACS, Sultan Moulay Slimane University, MATIC Research Team: Applied Mathematics and Information and Communication Technologie

⁵2Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science

⁶Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Morocco.

چکیده

This study explores a continuous spatio-temporal mathematical model to illustrate the dynamics of Monkeypox virus spread across various regions, considering both human and animal hosts. We propose a comprehensive strategy that includes awareness campaigns, security measures, and health interventions in areas where the virus is prevalent. The goal is to reduce transmission between humans and animals, thereby decreasing human infections and eradicating the virus in animal populations. Our model, which integrates spatial variables, accurately reflects the geographical spread of the virus and the impact of interventions, followed by the implementation and analysis of an applicable optimal control problem. Optimal control theory methods are applied in this work to demonstrate the existence of optimal control and the necessary conditions for optimality. We conduct numerical simulations using MATLAB with the forward-backward sweep method, revealing the efficiency of strategies focused on protecting vulnerable populations, preventing contact with infected individuals and animals, and promoting the use of quarantine facilities as the most effective means to control the spread of the Monkeypox virus. Additionally, the study examines the socio-economic impacts of the virus and the benefits of timely intervention. This approach provides valuable insights for policymakers and public health officials in managing and controlling the spread of Monkeypox.

کلیدواژه‌ها

Monkeypox؛ Optimal control؛ Spatio-temporal model؛ Mathematical model؛ optimization

مراجع

[1] Amaral, A.V.R., González, J.A. and Moraga, P. Spatio-temporal modeling of infectious diseases by integrating compartment and point process models, Stoch. Environ. Res. Risk Assess. 37 (4) (2023) 1519–1533.
[2] Barbu, V. Mathematical methods in optimization of differential systems, Vol. 310: Springer Science and Business Media, 2012.
[3] Baroudi, M., Gourram, H., Labzai, A. and Belam, M. Mathematical modeling and Monkeypox’s optimal control strategy, Commun. Math. Biol. Neurosci. 2023 (2023) Article ID 110.
[4] Bleichrodt, A., Dahal, S., Maloney, K., Casanova, L., Luo, R. and Chowell, G. Real-time forecasting the trajectory of Monkeypox outbreaks at the national and global levels, July–October 2022, BMC Med. 21 (1) (2023)19.
[5] Bourdaud, G. Le calcul fonctionnel dans les espaces de Sobolev, Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi Séminaire Goulaouic-Schwartz (1991) 1–4.
[6] Chen, D., Moulin, B. and Wu, J. Analyzing and modeling spatial and temporal dynamics of infectious diseases: Wiley Online Library, 2015.
[7] Falb, P.L. and Athans, M. Optimal control: An introduction to the theory and its applications, Dover Publications, 2006

[8] Gérard, P. Description du défaut de compacité de l’injection de Sobolev, ESAIM: Contr. Optim. Calculus Var. 3 (1998) 213–233.
[9] Hoff, N.A., Doshi, R.H., Colwell, B., Kebela-Illunga, B., Mukadi, P., Mossoko, M., Muyembe-Tamfum, J.J., Okitolonda-Wemakoy, E., LloydSmith, J. and Rimoin, A.W. Evolution of a disease surveillance system: an increase in reporting of human Monkeypox disease in the Democratic Republic of the Congo, 2001–2013, Int. J. Trop. Dis. Health, 25 (2)(2017).
[10] Islam, M.A., Sangkham, S., Tiwari, A., Vadiati, M., Hasan, M.N., Noor, S.T.A., Mumin, J., Bhattacharya, P. and Sherchan, S.P. Association between global Monkeypox cases and meteorological factors, Int. J. Environ. Res. Public Health, 19 (23) (2022) 15638.
[11] Liu, B., Farid, S., Ullah, S., Altanji, M., Nawaz, R. and Wondimagegnhu Teklu, S. Mathematical assessment of Monkeypox disease with the impact of vaccination using a fractional epidemiological modeling approach, Sci. Rep. 13 (1) (2023) 13550.
[12] Mandja, B.A.M., Brembilla, A., Handschumacher, P., Bompangue, D., Gonzalez, J.P., Muyembe, J.J. and Mauny, F. Temporal and spatial dynamics of Monkeypox in Democratic Republic of Congo, 2000–2015, EcoHealth 16 (2019) 476–487.
[13] Moumine, E.M., Balatif, O. and Rachik, M. Mathematical analysis and forecasting of controlled Spatio-temporal dynamics of the EG. 5 virus, Iranian Journal of Numerical Analysis and Optimization 14 (2) (2024) 500–521.
[14] Munir, T., Khan, M., Cheema, S.A., Khan, F., Usmani, A. and Nazir, M. ime series analysis and short-term forecasting of Monkeypox outbreak trends in the 10 major affected countries, BMC Infect. Dis. 24 (1) (2024) 16.
[15] Ozoliņš, V., Lai, R., Caflisch, R. and Osher, S. Compressed plane waves yield a compactly supported multiresolution basis for the Laplace operator, Proc. Natl. Acad. Sci. 111 (5) (2014) 1691–1696. 

[16] Pal, M., Mengstie, F. and Kandi, V. Epidemiology, diagnosis, and control of Monkeypox disease: A comprehensive review, Am. J. Infect. Dis. Microbiol. 5 (2) (2017) 94–99.
[17] Rodriguez, N. and Bertozzi, A. Local existence and uniqueness of solutions to a PDE model for criminal behavior, Math. Models Methods Appl. Sci. 20 (supp01) (2010) 1425–1457.
[18] Smouni, I., El Mansouri, A., Khajji, B., Labzai, A., Belam, M. and Tidli, Y. Mathematical modeling and analysis of a Monkeypox model, Commun. Math. Biol. Neurosci. 2023 (2023) Article ID 85.
[19] Stengel, R.F. Optimal control and estimation: Courier Corporation, 1994.
[20] Takhar, S.S. Epidemiologic and clinical characteristics of Monkeypox cases–United States, May 17-July 22, 2022, Ann. Emerg. Med. 81, (1) (2023) 31–34.
[21] Talisuna, A.O., Okiro, E.A., Yahaya, A.A., Stephen, M., Bonkoungou, B., Musa, E.O., Minkoulou, E.M., Okeibunor, J., Impouma, B., Djingarey, H.M. and YAO, N.D.K.M. Spatial and temporal distribution of infectious disease epidemics, disasters and other potential public health emergencies in the World Health Organisation Africa region, 2016–2018,
Glob. Health. 16 (2020) 1–12. 
[22] Wittenberg, R.W. Local dynamics and spatiotemporal chaos. The Kuramoto-Sivashinsky equation: A case study, Princeton University, 1998.
[23] Yang, S. Global solutions of nonlinear wave equations with large data, Sel. Math. 21 (2015) 1405–1427.
[24] Yinka-Ogunleye, A., Aruna, O., Dalhat, M., Ogoina, D., McCollum, A., Disu, Y., Mamadu, I., Akinpelu, A., Ahmad, A., Burga, J. and Ndoreraho, A., Outbreak of human Monkeypox in Nigeria in 2017–2018: a clinical and epidemiological report, Lancet Infect. Dis. 19 (8) (2019) 872–879. 

[25] Zebardast, A., Latifi, T., Shafiei-Jandaghi, N.Z., Gholami Barzoki, M. and Shatizadeh Malekshahi, S. Plausible reasons for the resurgence of Mpox (formerly Monkeypox): An overview, Trop. Dis. Travel Med. Vaccines. 9 (1) (2023) 23.