Transmission dynamics and stability of fractional order derivative model for COVID-19 epidemic with optimal control analysis

S. Suganya; V. Parthiban; R Kavikumar; Oh-Min Kwon; S. Suganya; V. Parthiban; R Kavikumar; Oh-Min Kwon

doi:10.3934/era.2025095

Electronic Research Archive

2025, Volume 33, Issue 4: 2172-2194. doi: 10.3934/era.2025095

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Transmission dynamics and stability of fractional order derivative model for COVID-19 epidemic with optimal control analysis

S. Suganya ¹,
V. Parthiban ^{1
,
,},
R Kavikumar ^{2,3
,
,},
Oh-Min Kwon ^{3
,
,}

1.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai 600127, Tamil Nadu, India
2.
Department of Mathematics, School of Advanced Science, VIT-AP University, Amaravati 522237, India
3.
School of Electrical Engineering, Chungbuk National University, Cheongju 28644, South Korea

Received: 26 January 2025 Revised: 19 March 2025 Accepted: 24 March 2025 Published: 15 April 2025

This present study analyzes COVID-19 transmission using a nonlinear mathematical model with a Caputo fractional derivative. By using fixed point theory, the existence and uniqueness of the solution are examined. We compute the basic reproduction number and investigate the stability analysis of the model. Approximate solutions are obtained using fractional Adam–Bashforth–Moulton method. A comprehensive exploration of optimal control is performed, utilizing one control parameter to investigate the fluctuations in the infected people under some conditions. The simulation results demonstrate the potential of fractional order derivatives with control parameter for a pandemic situation.
- fractional order model,
- Caputo derivative,
- stability,
- fractional optimal control,
- numerical simulations
Citation: S. Suganya, V. Parthiban, R Kavikumar, Oh-Min Kwon. Transmission dynamics and stability of fractional order derivative model for COVID-19 epidemic with optimal control analysis[J]. Electronic Research Archive, 2025, 33(4): 2172-2194. doi: 10.3934/era.2025095

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Abstract

This present study analyzes COVID-19 transmission using a nonlinear mathematical model with a Caputo fractional derivative. By using fixed point theory, the existence and uniqueness of the solution are examined. We compute the basic reproduction number and investigate the stability analysis of the model. Approximate solutions are obtained using fractional Adam–Bashforth–Moulton method. A comprehensive exploration of optimal control is performed, utilizing one control parameter to investigate the fluctuations in the infected people under some conditions. The simulation results demonstrate the potential of fractional order derivatives with control parameter for a pandemic situation.

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