A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1)
Corresponding Author
Gilberto González-Parra
Grupo de Matemática Multidisciplinar (GMM), Fac. de Ingeniería, Universidad de los Andes, Mérida, Venezuela
Centro de Investigaciones en Matemática Aplicada (CIMA), Universidad de los Andes, Mérida, Venezuela
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
Correspondence to: Gilberto González-Parra, Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA.
E-mail: [email protected]
Search for more papers by this authorAbraham J. Arenas
Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería, Colombia
Grupo Teseeo, Universidad del Sinú, Montería, Colombia
Search for more papers by this authorBenito M. Chen-Charpentier
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
Search for more papers by this authorCorresponding Author
Gilberto González-Parra
Grupo de Matemática Multidisciplinar (GMM), Fac. de Ingeniería, Universidad de los Andes, Mérida, Venezuela
Centro de Investigaciones en Matemática Aplicada (CIMA), Universidad de los Andes, Mérida, Venezuela
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
Correspondence to: Gilberto González-Parra, Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA.
E-mail: [email protected]
Search for more papers by this authorAbraham J. Arenas
Departamento de Matemáticas y Estadística, Universidad de Córdoba, Montería, Colombia
Grupo Teseeo, Universidad del Sinú, Montería, Colombia
Search for more papers by this authorBenito M. Chen-Charpentier
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
Search for more papers by this authorAbstract
In this paper, we propose a nonlinear fractional order model in order to explain and understand the outbreaks of influenza A(H1N1). In the fractional model, the next state depends not only upon its current state but also upon all of its historical states. Thus, the fractional model is more general than the classical epidemic models. In order to deal with the fractional derivatives of the model, we rely on the Caputo operator and on the Grünwald–Letnikov method to numerically approximate the fractional derivatives. We conclude that the nonlinear fractional order epidemic model is well suited to provide numerical results that agree very well with real data of influenza A(H1N1) at the level population. In addition, the proposed model can provide useful information for the understanding, prediction, and control of the transmission of different epidemics worldwide. Copyright © 2013 John Wiley & Sons, Ltd.
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