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<p>Obesity is the excessive accumulation of fat mass that negatively affects quality of life at multiple levels: health (physical and mental), society, economy, etc. It is a dangerous epidemic that affects developed and developing countries alike. In this article, we propose a continuous-time dynamic epidemiological model that describes the transmission of obesity within an infected population. By using the Routh-Hurwitz criteria and constructing Lyapunov functions, we obtain the local and global stability of the equilibrium both in the presence and absence of disease. We perform a sensitivity analysis to determine the contribution and impact of each model parameter on the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> </InlineEquation>. Finally, the theoretical results are illustrated by numerical simulation via Matlab.</p>

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Qualitative analysis and stability of a mathematical model for the spread of obesity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月16日

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  • Abdelbar El Mansouri,
  • Abderrahim Labzai,
  • Mohamed Belam

摘要

Obesity is the excessive accumulation of fat mass that negatively affects quality of life at multiple levels: health (physical and mental), society, economy, etc. It is a dangerous epidemic that affects developed and developing countries alike. In this article, we propose a continuous-time dynamic epidemiological model that describes the transmission of obesity within an infected population. By using the Routh-Hurwitz criteria and constructing Lyapunov functions, we obtain the local and global stability of the equilibrium both in the presence and absence of disease. We perform a sensitivity analysis to determine the contribution and impact of each model parameter on the basic reproduction number \(R_{0}\) . Finally, the theoretical results are illustrated by numerical simulation via Matlab.