Mathematical Modeling of SARS-CoV-2 Epidemics Using Fractional Calculus and Optimal Interventions

Authors

  • Nadeem Abbas Prince Sultan University
  • Wasfi Shatanawi Prince Sultan University
  • Syeda Alishwa Zanib Riphah International University

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6347

Keywords:

Fractional Differential Equations, Epidemic Disease, Stability analysis and Optimal control

Abstract

In December 2019, the SARS-CoV-2 (COVID-19) virus was identified and quickly spread worldwide, causing a major global health crisis. To investigate its transmission dynamics, we developed a ten-compartment mathematical model, named CoVCom10, which includes key stages such as asymptomatic (F), pre-symptomatic (E), and vaccinated (V ) individuals. The basic reproduction number (R0) has been calculated to evaluate how easily the virus can spread. We analyzed the local and global stability of the disease-free equilibrium and prove that the disease under control after vaccination when R0 < 1. A sensitivity analysis was conducted to assess the impact of key parameters, including the vaccination rate from susceptible individuals (β), trans-
mission from susceptible to pre-symptomatic individuals (φ), and the rate of vaccination from pre-symptomatic individuals (γ). To evaluate intervention strategies, we extended the model by incorporating time-dependent control variables representing vaccination (a1), hospitalization (a2), and isolation of asymptomatic individuals (a3). The Pontryagin Maximum Principle was applied to identify optimal control strategies. Numerical simulations reveal that these interventions significantly reduce virus transmission, particularly as the fractional-order parameter (ς) approaches 1, which aligns with observed real-world disease dynamics. The study emphasizes the effectiveness of integrated vaccination and treatment strategies in controlling the spread of COVID-19.

Author Biographies

  • Wasfi Shatanawi, Prince Sultan University

    He was working as a full professor in the Department of Mathematics at Hashemite University, Jordon. Now, he is working as a full professor in the Department of Mathematics at Prince Sultan University, Riyadh, Saudi Arabia. Their current project is the National University of Malaysia. He is highly cited in the year 2024. He also published many papers and achieved the Best Researcher award from Prince Sultan University.

  • Syeda Alishwa Zanib, Riphah International University

    Syeda Alishwa Zanib completed her MS at the Riphah International University Faisalabad Campus, Faisalabad, Pakistan. She is working as an Assistant Researcher at Riphah International University Faisalabad Campus, Faisalabad, Pakistan. She has published many articles in ISI highly impact factor journals.

Downloads

Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Nadeem Abbas, Wasfi Shatanawi, Syeda Alishwa Zanib

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Mathematical Modeling of SARS-CoV-2 Epidemics Using Fractional Calculus and Optimal Interventions. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6347. https://doi.org/10.29020/nybg.ejpam.v18i3.6347