Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia
Department of Mathematics, New Mexico Tech, Socorro, NM 87801, USA
Facultad de Ciencias, Departamento de Matemáticas, Universidad El Bosque, Edificio F, piso 2, Bogotá, Colombia
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019, USA
Facultad de Ing., Centro de Investigacion de Matemáticas Aplicada, Universidad de Los Andes, Mérida, Venezuela
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.
Received: 23 November 2018 / Revised: 27 December 2018 / Accepted: 28 December 2018 / Published: 3 January 2019
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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
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
. 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.
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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.
González-Parra GC, Aranda DF, Chen-Charpentier B, Díaz-Rodríguez M, Castellanos JE. Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia. Mathematical and Computational Applications. 2019; 24(1):6.
González-Parra, Gilberto C.; Aranda, Diego F.; Chen-Charpentier, Benito; Díaz-Rodríguez, Miguel; Castellanos, Jaime E. 2019. "Mathematical Modeling and Characterization of the Spread of Chikungunya in Colombia." Math. Comput. Appl. 24, no. 1: 6.
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