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Journal of Applied Nonlinear Dynamics 13(2) (2024) 211--222 | DOI:10.5890/JAND.2024.06.003

M. Arunkumar, R. Praveen Kumar, K. Murugesan

Department of Mathematics, National Institute of Technology, Tiruchirappalli, Tamil Nadu-620 015, India

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Abstract

In this paper, the Homotopy Analysis Method (HAM) is implemented to obtain the approximate solutions of a nonlinear system of ordinary differential equations such as the obesity epidemic model. The convergence theorem of HAM for the model as well as the regions of convergence derived from the $g$ curves are demonstrated. In addition, an optimal convergence control parameter has been determined. Numerical simulations of the model are carried out using MATLAB and then compared with the results of the Runge-Kutta (RK) method. The simulation results show that if the adult population follow a healthy lifestyle and physical exercises, it reduces the progression of becoming overweight and obese. The graphs and the tables exhibit the simplicity and the reliability of the method.

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