A SEIR Metapopulation Model for Mpox Transmission Dynamics in the DRC
DOI:
https://doi.org/10.30871/jaic.v10i1.11668Keywords:
Mpox, SEIR Metapopulation, Stability Analysis, Basic Reproduction Number, Sensitivity AnalysisAbstract
Understanding the mechanisms of infectious disease spread is a fundamental prerequisite for any control, management, or eradication strategy. This understanding relies on the rigorous integration of biological knowledge, mathematical tools, and computational resources, which enable in-depth analysis, the formulation of approximate numerical solutions, and the simulation of the temporal evolution of the pathological phenomenon. In this study, we develop an SEIR-type compartmental model to represent the transmission dynamics of Mpox, taking into account a metapopulation structure between two interconnected geographical areas, designated as patches 1 and 2. This model allows us to integrate the effects of interregional mobility on the spread of infection. The SageMath environment (version 9.3) was used to simulate viral dynamics within each patch, incorporating migration flows between the two regions. The system equilibria were determined and adjusted based on available data. The analysis focused on calculating the basic reproduction number, studying the stability of equilibria, and evaluating parameter sensitivity. The results suggest a gradual extinction of the disease in both patches, under certain conditions relating to mobility and recovery rates. Finally, this
investigation highlights the relevance of SageMath software as a powerful tool for exploring and simulating spatially structured epidemiological models, with the ability to adapt to a variety of contexts and pathologies.
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References
[1] S. Bowong and S. Bowong, ‘CAFHOMEC-BMGF 2024 Mod´elisation et analyse pour la sant´e des femmes’.
[2] S. Bowong, ‘Le modèle de Kermack et McKendrick’.
[3] E. P. S. Mbelambela, A. J. P. Wandja, A. F. Villanueva, N. D. Olamba, L. Omba, and S. M. J. Muchanga, ‘Clinical characteristics of suspected cases of human mpox (monkeypox) in Katako-Kombe, Democratic Republic of the Congo 2023: challenges and key responses’, Eur. J. Clin. Microbiol. Infect. Dis., vol. 44, no. 3, pp. 609–617, Mar. 2025, doi: 10.1007/s10096-024-05022-3.
[4] ‘8_Medecine_Generale_Pierre_Lea_these’.
[5] O. J. Peter, S. Kumar, N. Kumari, F. A. Oguntolu, K. Oshinubi, and R. Musa, ‘Transmission dynamics of Monkeypox virus: a mathematical modelling approach’, Model. Earth Syst. Environ., vol. 8, no. 3, pp. 3423–3434, Sept. 2022, doi: 10.1007/s40808-021-01313-2.
[6] R. A. Ahmad et al., ‘Modeling social interaction and metapopulation mobility of the COVID-19 pandemic in main cities of highly populated Java Island, Indonesia: An agent-based modeling approach’, Front. Ecol. Evol., vol. 10, p. 958651, Jan. 2023, doi: 10.3389/fevo.2022.958651.
[7] ‘Modélisation-mathématique-de-propagation-dune-épidémie’.
[8] M. A. Aziz-Alaoui et al., ‘Etude de Quelques Modèles Epidémiologiques de Métapopulations : Application au Paludisme et à la Tuberculose’.
[9] W. Cota, D. Soriano-Paños, A. Arenas, S. C. Ferreira, and J. Gómez-Gardeñes, ‘Infectious disease dynamics in metapopulations with heterogeneous transmission and recurrent mobility’, New J. Phys., vol. 23, no. 7, p. 073019, July 2021, doi: 10.1088/1367-2630/ac0c99.
[10] J. Arino, ‘Diseases in Metapopulations’, in Series in Contemporary Applied Mathematics, vol. 11, CO-PUBLISHED WITH HIGHER EDUCATION PRESS, 2009, pp. 64–122. doi: 10.1142/9789814261265_0003.
[11] M. J. Keeling, O. N. Bjørnstad, and B. T. Grenfell, ‘17. METAPOPULATION DYNAMICS OF’.
[12] M. M. Herman, P. G. Patience, N. Marcial, M. K. Lea, K. M. Peter, and C. M. Benjamin, ‘Analyzing and Controlling COVID-19 Using SageMath Toolbox: A case Study in the D.R. Congo’, vol. 9, no. 4.
[13] J. Arino, ‘Quelques notions d’épidémiologie mathématique’.
[14] A. Apolloni, C. Poletto, J. J. Ramasco, P. Jensen, and V. Colizza, ‘Metapopulation epidemic models with heterogeneous mixing and travel behaviour’, Theor. Biol. Med. Model., vol. 11, no. 1, p. 3, Dec. 2014, doi: 10.1186/1742-4682-11-3.
[15] S. Léger, ‘PROTOCOLE DE TRAITEMENT DE MONKEYPOX SIMPLE ET COMPLIQUE’.
[16] ‘Mpox_USPPI-2024’.
[17] Z. Shuai and P. Van Den Driessche, ‘Global Stability of Infectious Disease Models Using Lyapunov Functions’, SIAM J. Appl. Math., vol. 73, no. 4, pp. 1513–1532, Jan. 2013, doi: 10.1137/120876642.
[18] D. Bichara, ‘Étude de modèles épidémiologiques: Stabilité, observation et estimation de paramètres’.
[19] E. J. Dansu and H. Seno, ‘A model for epidemic dynamics in a community with visitor subpopulation’, J. Theor. Biol., vol. 478, pp. 115–127, Oct. 2019, doi: 10.1016/j.jtbi.2019.06.020.
[20] S. Wang, B. Haegeman, and M. Loreau, ‘Dispersal and metapopulation stability’, PeerJ, vol. 3, p. e1295, Oct. 2015, doi: 10.7717/peerj.1295.
[21] M. Maliyoni, H. D. Gaff, K. S. Govinder, and F. Chirove, ‘Multipatch stochastic epidemic model for the dynamics of a tick-borne disease’, Front. Appl. Math. Stat., vol. 9, p. 1122410, June 2023, doi: 10.3389/fams.2023.1122410.
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Copyright (c) 2026 Kasende Mundeke Peter, Herman MATONDO MANANGA, Milolo Kanumuambidi Lea Irène, Pokuaa Gambrah Patience
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