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<p>Dental caries is a significant public health concern globally. This research presents a mathematical model for simulating the spread of dental caries using fractional differential equations. The model incorporates fractional-order dynamics to better understand and manage the transmission and development of the disease. Numerical solutions are computed using the Adams–Bashforth–Moulton method. The study includes an examination of the model’s solutions to ensure their existence and uniqueness, and to assess the local stability of equilibrium points. Stability analysis is conducted through the Ulam–Hyers process, offering valuable insights into how the system behaves with varying parameters. The results illustrate the model’s effectiveness in accurately representing the spread of dental caries, with graphical analyses highlighting the impact of different fractional orders on infection spread, thereby improving our understanding of the model’s performance.</p>

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Numerical and Theoretical Insights into Fractional Dental Caries Infection Model

  • 期刊论文

  • 发表日期：

    2025年5月5日

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  • Sagar R. Khirsariya,
  • Jignesh P. Chauhan

摘要

Dental caries is a significant public health concern globally. This research presents a mathematical model for simulating the spread of dental caries using fractional differential equations. The model incorporates fractional-order dynamics to better understand and manage the transmission and development of the disease. Numerical solutions are computed using the Adams–Bashforth–Moulton method. The study includes an examination of the model’s solutions to ensure their existence and uniqueness, and to assess the local stability of equilibrium points. Stability analysis is conducted through the Ulam–Hyers process, offering valuable insights into how the system behaves with varying parameters. The results illustrate the model’s effectiveness in accurately representing the spread of dental caries, with graphical analyses highlighting the impact of different fractional orders on infection spread, thereby improving our understanding of the model’s performance.