{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T12:49:29Z","timestamp":1792068569949,"version":"4.4.0"},"reference-count":24,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MBE"],"published-print":{"date-parts":[[2026]]},"DOI":"10.3934\/mbe.2026011","type":"journal-article","created":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T12:49:46Z","timestamp":1767098986000},"page":"266-290","source":"Crossref","is-referenced-by-count":1,"title":["Stochastic modeling, analysis, and simulation of Dengue in Valle del Cauca: A case study"],"prefix":"10.3934","volume":"23","author":[{"given":"Diego Alejandro","family":"Becerra-Becerra","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"name":"Department of Statistics, Universidad Nacional de Colombia, Bogot\u00e1, Colombia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jhonier","family":"Rangel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Viswanathan","family":"Arunachalam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"name":"Program of Statistics, Universidad ECCI, Bogot\u00e1, Colombian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2026011-1","unstructured":"OMS, <i>Dengue y Dengue grave<\/i>, <i>OMS<\/i>, 2024. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.who.int\/es\/news-room\/fact-sheets\/detail\/Dengue-and-severe-Dengue\">https:\/\/www.who.int\/es\/news-room\/fact-sheets\/detail\/Dengue-and-severe-Dengue<\/ext-link>"},{"key":"key-10.3934\/mbe.2026011-2","doi-asserted-by":"crossref","unstructured":"O. A. Montesinos-L\u00f3pez, C. M. Hern\u00e1ndez-Su\u00e1rez, Modelos matem\u00e1ticos para enfermedades infecciosas, <i>Salud Publica Mex.<\/i>, <b>49<\/b> (2007), 218\u2013226.","DOI":"10.1590\/S0036-36342007000300007"},{"key":"key-10.3934\/mbe.2026011-3","doi-asserted-by":"publisher","unstructured":"Y. Guo, T. Li, Modeling the competitive transmission of the Omicron strain and Delta strain of COVID-19, <i>J. Math. Anal. Appl.<\/i>, <b>526<\/b> (2023), 127283. https:\/\/doi.org\/10.1016\/j.jmaa.2023.127283","DOI":"10.1016\/j.jmaa.2023.127283"},{"key":"key-10.3934\/mbe.2026011-4","doi-asserted-by":"publisher","unstructured":"A. Gray, D. Greenhalgh, L. Hu, X. Mao, J. Pan, A stochastic differential equation SIS epidemic model, <i>SIAM J. Appl. Math.<\/i>, <b>71<\/b> (2011), 876\u2013902. https:\/\/doi.org\/10.1137\/10081856X","DOI":"10.1137\/10081856X"},{"key":"key-10.3934\/mbe.2026011-5","doi-asserted-by":"publisher","unstructured":"A. R\u00edos-Guti\u00e9rrez, S. Torres, V. Arunachalam, Studies on the basic reproduction number in stochastic epidemic models with random perturbations, <i>Adv. Differ. Equ.<\/i>, <b>2021<\/b> (2021), 288. https:\/\/doi.org\/10.1186\/s13662-021-03445-2","DOI":"10.1186\/s13662-021-03445-2"},{"key":"key-10.3934\/mbe.2026011-6","doi-asserted-by":"publisher","unstructured":"Y. Sabbar, A. Din, D. Kiouach, Influence of fractal\u2013fractional differentiation and independent quadratic L\u00e9vy jumps on the dynamics of a general epidemic model with vaccination strategy, <i>Chaos Solitons Fractals<\/i>, <b>171<\/b> (2023), 113434. https:\/\/doi.org\/10.1016\/j.chaos.2023.113434","DOI":"10.1016\/j.chaos.2023.113434"},{"key":"key-10.3934\/mbe.2026011-7","doi-asserted-by":"publisher","unstructured":"Y. Sabbar, Refining extinction criteria in a complex multi-stage epidemic system with non-Gaussian L\u00e9vy noise, <i>Commun. Nonlinear Sci. Numer. Simul.<\/i>, <b>149<\/b> (2025), 108911. https:\/\/doi.org\/10.1016\/j.cnsns.2025.108911","DOI":"10.1016\/j.cnsns.2025.108911"},{"key":"key-10.3934\/mbe.2026011-8","unstructured":"I. N. de Salud, <i>Sistema de Vigilancia en Salud P\u00fablica (SIVIGILA)<\/i>, 2025. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/portalsivigila.ins.gov.co\/\">https:\/\/portalsivigila.ins.gov.co\/<\/ext-link>."},{"key":"key-10.3934\/mbe.2026011-9","unstructured":"D. Pe\u00f1a, An\u00e1lisis de series temporales, Alianza, 2005."},{"key":"key-10.3934\/mbe.2026011-10","doi-asserted-by":"publisher","unstructured":"A. Din, T. Khan, Y. Li, H. Tahir, A. Khan, W. A. Khan, Mathematical analysis of Dengue stochastic epidemic model, <i>Results Phys.<\/i>, <b>20<\/b> (2021), 103719. https:\/\/doi.org\/10.1016\/j.rinp.2020.103719","DOI":"10.1016\/j.rinp.2020.103719"},{"key":"key-10.3934\/mbe.2026011-11","doi-asserted-by":"publisher","unstructured":"M. Z. Ndii, Y. A. Adi, B. S. Djahi, Deterministic and stochastic Dengue epidemic model: Exploring the probability of extinction, <i>Barekeng: J. Ilmu Mat. Ter.<\/i>, <b>16<\/b> (2022), 583\u2013596. https:\/\/doi.org\/10.30598\/barekengvol16iss2pp583-596","DOI":"10.30598\/barekengvol16iss2pp583-596"},{"key":"key-10.3934\/mbe.2026011-12","unstructured":"I. Karatzas, S. E. Shreve, <i>Brownian Motion and Stochastic Calculus<\/i>, 2nd edition, Springer, 1991. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-1-4612-0949-2\">https:\/\/doi.org\/10.1007\/978-1-4612-0949-2<\/ext-link>"},{"key":"key-10.3934\/mbe.2026011-13","unstructured":"P. E. Kloeden, E. Platen, <i>Numerical Solution of Stochastic Differential Equations<\/i>, Springer, 1992. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-3-662-12616-5\">https:\/\/doi.org\/10.1007\/978-3-662-12616-5<\/ext-link>"},{"key":"key-10.3934\/mbe.2026011-14","doi-asserted-by":"publisher","unstructured":"X. Mao, C. Yuan, J. Zou, Stochastic differential delay equations of population dynamics, <i>J. Math. Anal. Appl.<\/i>, <b>304<\/b> (2005), 296\u2013320. https:\/\/doi.org\/10.1016\/j.jmaa.2004.09.027","DOI":"10.1016\/j.jmaa.2004.09.027"},{"key":"key-10.3934\/mbe.2026011-15","doi-asserted-by":"publisher","unstructured":"G. Maruyama, Continuous Markov processes and stochastic equations, <i>Rend. Circ. Mat. Palermo<\/i>, <b>4<\/b> (1955), 48\u201390. https:\/\/doi.org\/10.1007\/BF02846028","DOI":"10.1007\/BF02846028"},{"key":"key-10.3934\/mbe.2026011-16","unstructured":"DANE, <i>Estad\u00edsticas vitales: Nacimientos<\/i>, 2023. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.dane.gov.co\/index.php\/estadisticas-por-tema\/salud\">https:\/\/www.dane.gov.co\/index.php\/estadisticas-por-tema\/salud<\/ext-link>"},{"key":"key-10.3934\/mbe.2026011-17","doi-asserted-by":"publisher","unstructured":"M. Andraud, N. Hens, C. Marais, P. Beutels, Dynamic epidemiological models for Dengue transmission: A systematic review of structural approaches, <i>PLoS ONE<\/i>, <b>7<\/b> (2012), e49085. https:\/\/doi.org\/10.1371\/journal.pone.0049085","DOI":"10.1371\/journal.pone.0049085"},{"key":"key-10.3934\/mbe.2026011-18","doi-asserted-by":"publisher","unstructured":"M. K. Enduri, S. Jolad, Dynamics of Dengue disease with human and vector mobility, <i>Spatial Spatio-temporal Epidemiol.<\/i>, <b>25<\/b> (2018), 57\u201366. https:\/\/doi.org\/10.1016\/j.sste.2018.03.001","DOI":"10.1016\/j.sste.2018.03.001"},{"key":"key-10.3934\/mbe.2026011-19","doi-asserted-by":"publisher","unstructured":"D. P. Lizarralde-Bejarano, S. Arboleda-S\u00e1nchez, M. E. Puerta-Yepes, Understanding epidemics from mathematical models: Details of the 2010 Dengue epidemic in Bello (Antioquia, Colombia), <i>Appl. Math. Modell.<\/i>, <b>43<\/b> (2017), 566\u2013578. https:\/\/doi.org\/10.1016\/j.apm.2016.11.022","DOI":"10.1016\/j.apm.2016.11.022"},{"key":"key-10.3934\/mbe.2026011-20","unstructured":"DANE, <i>Identidad gr\u00e1fica del Censo Nacional de Poblaci\u00f3n y Vivienda 2018<\/i>, 2019. Available from: <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/sitios.dane.gov.co\/cnpv\/\">https:\/\/sitios.dane.gov.co\/cnpv\/<\/ext-link>"},{"key":"key-10.3934\/mbe.2026011-21","doi-asserted-by":"publisher","unstructured":"M. A. Branch, T. F. Coleman, Y. Li, A subspace, interior, and conjugate gradient method for large-scale bound-constrained minimization problems, <i>SIAM J. Sci. Comput.<\/i>, <b>21<\/b> (1999), 1\u201323. https:\/\/doi.org\/10.1137\/S1064827595289108","DOI":"10.1137\/S1064827595289108"},{"key":"key-10.3934\/mbe.2026011-22","doi-asserted-by":"publisher","unstructured":"P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, et al., SciPy 1.0: Fundamental algorithms for scientific computing in Python, <i>Nat. Methods<\/i>, <b>17<\/b> (2020), 261\u2013272. https:\/\/doi.org\/10.1038\/s41592-019-0686-2","DOI":"10.1038\/s41592-019-0686-2"},{"key":"key-10.3934\/mbe.2026011-23","unstructured":"P. J. Brockwell, R. A. Davis, <i>Time Series: Theory and Methods<\/i>, Springer, 1991. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-1-4419-0320-4\">https:\/\/doi.org\/10.1007\/978-1-4419-0320-4<\/ext-link>"},{"key":"key-10.3934\/mbe.2026011-24","unstructured":"P. J. Brockwell, R. A. Davis, <i>Introduction to Time Series and Forecasting<\/i>, Springer, 2016. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/doi.org\/10.1007\/978-3-319-29854-2\">https:\/\/doi.org\/10.1007\/978-3-319-29854-2<\/ext-link>"}],"container-title":["Mathematical Biosciences and Engineering"],"original-title":[],"link":[{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2026011?viewType=html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T12:52:44Z","timestamp":1767099164000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.aimspress.com\/article\/doi\/10.3934\/mbe.2026011"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.3934\/mbe.2026011","relation":{},"ISSN":["1551-0018"],"issn-type":[{"value":"1551-0018","type":"print"}],"subject":[],"published":{"date-parts":[[2026]]}}}