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This study analyzes a fractional-order SEIR epidemic model to predict infectious disease outbreaks. It determines disease stability based on the basic reproduction number (R0), crucial for forecasting potential epidemics.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Fractional Calculus

Background:

  • Infectious disease modeling is crucial for public health.
  • The SEIR (Susceptible-Infected-Recovered) model is a standard framework.
  • Fractional-order models offer enhanced complexity for disease dynamics.

Purpose of the Study:

  • To analyze a generalized fractional-order SEIR epidemic model.
  • To determine conditions for disease stability and equilibrium.
  • To incorporate individual behavior into epidemic forecasting.

Main Methods:

  • Utilized a generalized fractional-order SEIR model.
  • Calculated the basic reproduction number (R0) using the next-generation matrix spectral radius.
  • Applied geometric methods to analyze equilibrium stability.

Main Results:

  • Disease-free equilibrium is stable when R0 < 1.
  • Endemic equilibrium is stable when R0 > 1.
  • Established conditions for local progressive stability of both equilibria.

Conclusions:

  • The fractional-order SEIR model provides insights into infectious disease dynamics.
  • The basic reproduction number is a key determinant of epidemic persistence.
  • The model's findings are vital for predicting and managing disease outbreaks.