Journal of Applied Mathematics
Volume 2008 (2008), Article ID 640154, 14 pages
Research Article

A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics

Rafael J. Villanueva,1 Abraham J. Arenas,2 and Gilberto González-Parra3

1Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, 2a, P.O. Box 22012, Camino de Vera s/n, 46022 Valencia, Spain
2Departamento de Matemática Aplicada, Universidad de Córdoba, Montería, Ciudad Universitaria Carrera 6 No. 76-103, CP 354, Montería, Colombia
3Departamento de Cálculo, Universidad de los Andes, Mérida 5101, Venezuela

Received 17 June 2008; Accepted 14 November 2008

Academic Editor: Heinz H. Bauschke

Copyright © 2008 Rafael J. Villanueva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The obesity epidemic is considered a health concern of paramount importance in modern society. In this work, a nonstandard finite difference scheme has been developed with the aim to solve numerically a mathematical model for obesity population dynamics. This interacting population model represented as a system of coupled nonlinear ordinary differential equations is used to analyze, understand, and predict the dynamics of obesity populations. The construction of the proposed discrete scheme is developed such that it is dynamically consistent with the original differential equations model. Since the total population in this mathematical model is assumed constant, the proposed scheme has been constructed to satisfy the associated conservation law and positivity condition. Numerical comparisons between the competitive nonstandard scheme developed here and Euler's method show the effectiveness of the proposed nonstandard numerical scheme. Numerical examples show that the nonstandard difference scheme methodology is a good option to solve numerically different mathematical models where essential properties of the populations need to be satisfied in order to simulate the real world.