Eur. Phys. J. Plus (2017) 132: 257
https://doi.org/10.1140/epjp/i2017-11512-y

Regular Article

Optimal solutions for the evolution of a social obesity epidemic model

¹ Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan
² Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

^* e-mail: umarkhan@ciit.net.pk

Received: 11 April 2017
Accepted: 26 April 2017
Published online: 12 June 2017

Abstract

In this work, a novel modification in the traditional homotopy perturbation method (HPM) is proposed by embedding an auxiliary parameter in the boundary condition. The scheme is used to carry out a mathematical evaluation of the social obesity epidemic model. The incidence of excess weight and obesity in adulthood population and prediction of its behavior in the coming years is analyzed by using a modified algorithm. The proposed method increases the convergence of the approximate analytical solution over the domain of the problem. Furthermore, a convenient way is considered for choosing an optimal value of auxiliary parameters via minimizing the total residual error. The graphical comparison of the obtained results with the standard HPM explicitly reveals the accuracy and efficiency of the developed scheme.