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<p>The fractional SIR epidemic model with logistic growth and Holling II-type treatment and incidence rates demonstrates several behaviors analogous to its integer-order counterpart. This highlights the model’s ability to capture the classical dynamics of the original system while introducing new complexities as the fractional-order parameter is varied. Notably, the stability of the equilibria is significantly influenced by the fractional order, leading to potential Hopf-like bifurcations as this parameter changes. Our study provides a comprehensive analysis of the model’s solutions, stability conditions, and bifurcation phenomena, supported by numerical simulations. These findings offer valuable insights into the dynamics of disease spread and treatment, paving the way for further exploration and application of fractional calculus in epidemiological modeling.</p>

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SIR model with logistic growth, non-linear incidence and saturated treatment based on fractional-order caputo derivatives

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • Roberto Carlos Balcázar-Araiza,
  • Eric José Ávila-Vales,
  • Gerardo Emilio García-Almeida

摘要

The fractional SIR epidemic model with logistic growth and Holling II-type treatment and incidence rates demonstrates several behaviors analogous to its integer-order counterpart. This highlights the model’s ability to capture the classical dynamics of the original system while introducing new complexities as the fractional-order parameter is varied. Notably, the stability of the equilibria is significantly influenced by the fractional order, leading to potential Hopf-like bifurcations as this parameter changes. Our study provides a comprehensive analysis of the model’s solutions, stability conditions, and bifurcation phenomena, supported by numerical simulations. These findings offer valuable insights into the dynamics of disease spread and treatment, paving the way for further exploration and application of fractional calculus in epidemiological modeling.