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A Preliminary Mathematical Model for the Dynamic Transmission of Dengue, Chikungunya and Zika
Current Issue
Volume 3, 2016
Issue 2 (April)
Pages: 11-15   |   Vol. 3, No. 2, April 2016   |   Follow on         
Paper in PDF Downloads: 283   Since Jun. 24, 2016 Views: 2003   Since Jun. 24, 2016
Authors
[1]
Raúl Isea, Institute of Advanced Studies – IDEA, Hoyo de la Puerta, Baruta, Venezuela.
[2]
Karl E. Lonngren, Department of Electrical and Computer Engineering, University of Iowa, Iowa City, Iowa, USA.
Abstract
Aedes aegypti is a known vector of Dengue, Chikungunya and Zika and the goal of this study is to propose the first mathematical model to describe the dynamic transmission of these three diseases. We present two preliminary models that consist of the SEIR model for the human populations and an SEI model for the vector to describe (a) the single transmission dynamics of dengue, Chikungunya or Zika, and (b) any possible coinfection between two diseases in the same population. In order to do that, we obtain an analytical solution of the system of 17 and 30 coupled differential equations for each model respectively, and later obtain the eigenvalues by analyzing the Jacobian matrix in order to begin the development of a surveillance system to prevent the spread of these three diseases.
Keywords
Epidemic, Differential Equation, Dengue, Chikungunya, Zika, Aedes aegypti
Reference
[1]
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[2]
Cardoso CW, Paploski IAD, Kikuti M, Rodrigues MS, Silva MMO, et al. Outbreak of Exanthematous Illness Associated with Zika, Chikungunya, and Dengue viruses, Salvador, Brazil, Emerg Infect Dis 2015; 21(12): 2274-2276.
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[6]
Villamil-Gómez WE, González-Camargo O, Rodriguez-Ayubi J, Zapata-Serpa D, Rodriguez-Morales AJ. Dengue, Chikungunya and Zika coinfection in a patient from Colombia. J Infect Public Health 2016; pii: S1876-0341.
[7]
Isea R. Analysis of an SEIR-SEI four-strain epidemic dengue model with primary and secondary infections. Revista Electrónica Conocimiento Libre y Licenciamiento (CLIC) 2014; 7: 3-7.
[8]
Janreung S and Chinviriyasit W. Dengue Fever with Two Strains in Thailand. IJAPM 2014; 4(1): 55-61.
[9]
Isea R and Lonngren KE. A Mathematical Model of Cancer Under Radiotherapy. International Journal of Public Health Research 2015; 3(6): 340-344.
[10]
Isea R and Mayo-García R. Mathematical analysis of the spreading of a rumor among different subgroups of spreaders. Pure and Applied Mathematical Letters. An International Journal 2015; 2015: 50-54.
[11]
Isea R. Análisis matemático de la difusión de un rumor entre dos grupos de personas. Revista Electrónica Conocimiento Libre y Licenciamiento (CLIC) 2015; 8: 85-89.
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