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Numerical simulation of a normalized time-fractional SUC epidemic model
Chaeyoung Lee1, Jyoti2, Soobin Kwak3
1Department of Mathematics, Kyonggi University, Suwon, Republic of Korea.
Computer Methods in Biomechanics and Biomedical Engineering
|September 16, 2025
Summary
This study introduces a fractional calculus epidemic model, revealing how memory effects influence disease spread. Lower fractional orders speed up susceptible decline and lower infection peaks, while higher orders prolong outbreaks.
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.
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