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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Fractional Calculus

Background:

  • Traditional epidemic models often assume local time interactions.
  • Memory effects and non-local interactions are crucial for understanding complex disease dynamics.
  • Fractional calculus offers a framework to incorporate these memory effects.

Purpose of the Study:

  • To develop a normalized time-fractional susceptible-unidentified infected-confirmed (SUC) epidemic model.
  • To investigate the impact of memory effects on epidemic transmission dynamics.
  • To analyze the influence of fractional orders and confirmation parameters on outbreak progression.

Main Methods:

  • Developed a normalized time-fractional SUC epidemic model using fractional calculus.
  • Incorporated memory effects to capture non-local time interactions.
  • Conducted numerical simulations to explore model behavior under varying parameters.

Main Results:

  • Smaller fractional orders accelerate susceptible decline and lead to faster, lower infection peaks.
  • Larger fractional orders result in slower, oscillatory declines and delayed, prolonged outbreaks.
  • Higher confirmation parameters significantly reduce infection spread and peak case numbers.

Conclusions:

  • Fractional calculus effectively models memory effects in epidemics.
  • Fractional orders critically influence epidemic trajectory, from peak timing to duration.
  • The confirmation parameter is a key factor in controlling epidemic spread and severity.