A Nonstandard Dynamically Consistent Numerical Scheme Applied to Obesity Dynamics

Abstract

}The obesity epidemic is considered a health concern of paramount importancein modern society. In this work, a nonstandard finite differencescheme has been developed with the aim to solve numerically a mathematicalmodel for obesity population dynamics. This interacting populationmodel represented as a system of coupled nonlinear ordinary differentialequations is used to analyze, understand, and predict the dynamics of obesitypopulations. The construction of the proposed discrete scheme is developedsuch that it is dynamically consistent with the original differentialequations model. Since the total population in this mathematical modelis assumed constant, the proposed scheme has been constructed to satisfythe associated conservation law and positivity condition. Numericalcomparisons between the competitive nonstandard scheme developed hereand Euler's method show the effectiveness of the proposed nonstandardnumerical scheme. Numerical examples show that the nonstandard differencescheme methodology is a good option to solve numerically differentmathematical models where essential properties of the populations need tobe satisfied in order to simulate the real world.