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Open AccessArticle

Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia

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Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA
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Facultad de Ciencias, Departamento de Matemáticas, Universidad El Bosque, Edificio F, piso 2, Bogotá, Colombia
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Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
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Facultad de Ing., Centro de Investigacion de Matemáticas Aplicada, Universidad de Los Andes, Mérida, Venezuela
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Grupo de Virologia, Facultad de Ciencias, Universidad El Bosque, Av. Carrera 9 No. 131-A-02, Bogotá, Colombia
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2019, 24(1), 6; https://doi.org/10.3390/mca24010006
Received: 23 November 2018 / Revised: 27 December 2018 / Accepted: 28 December 2018 / Published: 3 January 2019
(This article belongs to the Special Issue Mathematical Modelling in Engineering & Human Behaviour 2018)
The Chikungunya virus is the cause of an emerging disease in Asia and Africa, and also in America, where the virus was first detected in 2006. In this paper, we present a mathematical model of the Chikungunya epidemic at the population level that incorporates the transmission vector. The epidemic threshold parameter R 0 for the extinction of disease is computed using the method of the next generation matrix, which allows for insights about what are the most relevant model parameters. Using Lyapunov function theory, some sufficient conditions for global stability of the the disease-free equilibrium are obtained. The proposed mathematical model of the Chikungunya epidemic is used to investigate and understand the importance of some specific model parameters and to give some explanation and understanding about the real infected cases with Chikungunya virus in Colombia for data belonging to the year 2015. In this study, we were able to estimate the value of the basic reproduction number R 0 . We use bootstrapping and Markov chain Monte Carlo techniques in order to study parameters’ identifiability. Finally, important policies and insights are provided that could help government health institutions in reducing the number of cases of Chikungunya in Colombia. View Full-Text
Keywords: Chikungunya disease; mathematical modeling; nonlinear dynamical systems; numerical simulations; parameter estimation; Markov chain Monte Carlo Chikungunya disease; mathematical modeling; nonlinear dynamical systems; numerical simulations; parameter estimation; Markov chain Monte Carlo
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González-Parra, G.C.; Aranda, D.F.; Chen-Charpentier, B.; Díaz-Rodríguez, M.; Castellanos, J.E. Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia. Math. Comput. Appl. 2019, 24, 6.

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