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A nonstandard dynamically consistent numerical scheme applied to obesity dynamics. (English) Zbl 1157.92028

Summary: 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.

MSC:

92D30 Epidemiology
65L12 Finite difference and finite volume methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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References:

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