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Fractional-order epidemic modeling with a deep neural network framework.

Pooja Jangir1, Garima Agarwal2, Kottakkaran Sooppy Nisar3,4

  • 1Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, India.

Scientific Reports
|March 27, 2026
PubMed
Summary

This study introduces a new fractional-order epidemiological model to better capture long-term memory effects in infectious disease dynamics. The model, validated by deep neural networks, improves understanding of disease transmission and control strategies.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Dynamical Systems

Background:

  • Infectious diseases pose a significant global health threat, necessitating accurate modeling for effective public health planning.
  • Traditional epidemiological models often fail to capture complex dynamics and long-term memory effects crucial for understanding disease spread.
  • Accurate disease modeling is essential for predicting outbreaks and informing public health interventions.

Purpose of the Study:

  • To propose a novel fractional-order Susceptible-Infectious-Treated-Recovered (SITR) epidemiological model incorporating a saturated incidence function and Caputo derivative.
  • To analyze the qualitative behavior of the model, including positivity, boundedness, and biological feasibility of solutions.
  • To calculate and analyze the basic reproduction number and equilibrium points to understand disease transmission dynamics and control conditions.

Main Methods:

  • A fractional-order SITR model with a saturated incidence function using the Caputo derivative was developed.
  • Qualitative analysis was performed to ensure biological feasibility and epidemiological relevance.
  • The model was numerically solved using the Adams-Bashforth-Moulton predictor-corrector method.
  • Bayesian Regularized Deep Neural Networks (BR-DNN) were employed as a data-driven surrogate solver for validation and efficiency.

Main Results:

  • The fractional-order model successfully incorporates long-term memory effects into epidemiological dynamics.
  • Qualitative tests confirmed the positivity, boundedness, and biological feasibility of the model's solutions.
  • The basic reproduction number and stability of equilibrium points were determined, providing insights into disease persistence and control.
  • Numerical solutions and BR-DNN surrogate model predictions showed high agreement, validating the proposed framework.

Conclusions:

  • The developed fractional-order SITR model offers a more comprehensive approach to modeling infectious diseases by accounting for memory-dependent effects.
  • The integration of BR-DNN provides an efficient and validated method for solving complex epidemiological models.
  • This framework enhances our ability to understand and predict epidemic dynamics, aiding in the development of effective public health strategies.