Mathematical Analysis of a Fractional SEIQHRV COVID-19 Model with Optimal Control and Public Health Interventions

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DOI: https://doi.org/10.28924/2291-8639-24-2026-355
Published: Oct 26, 2026
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Amit Jain, V.P. Murugan, N. Avinash, Vediyappan Govindan, Siriluk Donganont, Mathematical Analysis of a Fractional SEIQHRV COVID-19 Model with Optimal Control and Public Health Interventions, Int. J. Anal. Appl., 24 (2026), 355.

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Amit Jain, V.P. Murugan, N. Avinash, Vediyappan Govindan, Siriluk Donganont

Abstract

This paper develops a seven-compartment fractional-order SEIQHRV model for COVID-19 transmission, with susceptible, exposed, infected, quarantined, hospitalized, recovered, and vaccinated classes and Caputo derivatives capturing memory effects. Three controls representing vaccination, quarantine-isolation, and clinical treatment are incorporated. Well-posedness, positivity, and boundedness are proved; the reproduction number, its sensitivity indices, a controlled threshold, and the endemic equilibrium are derived explicitly; and existence of optimal controls and the fractional Pontryagin Maximum Principle with exact costate equations are established. Simulations by a forward-backward sweep with an Adams-type scheme, verified by convergence and gradient tests, show that combined control is most effective, that vaccination and quarantine are complementary, and that smaller fractional orders yield flatter but more persistent epidemics.

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References

  1. O.P. Agrawal, A General Formulation and Solution Scheme for Fractional Optimal Control Problems, Nonlinear Dyn. 38 (2004), 323–337. https://doi.org/10.1007/s11071-004-3764-6.
  2. E. Ahmed, A.M.A. El-Sayed, H.A.A. El-Saka, Equilibrium Points, Stability and Numerical Solutions of Fractional-Order Predator–Prey and Rabies Models, J. Math. Anal. Appl. 325 (2007), 542–553. https://doi.org/10.1016/j.jmaa.2006.01.087.
  3. S.H. Abel-Gaid, A.H. Qamlo, B.G. Mohamed, Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems, Fractal Fract. 8 (2024), 84. https://doi.org/10.3390/fractalfract8020084.
  4. M. Caputo, Linear Models of Dissipation Whose Q Is Almost Frequency Independent–II, Geophys. J. Int. 13 (1967), 529–539. https://doi.org/10.1111/j.1365-246X.1967.tb02303.x.
  5. T.-M. Chen, J. Rui, Q.-P. Wang, Z.-Y. Zhao, J.-A. Cui, et al., A Mathematical Model for Simulating the Phase-Based Transmissibility of a Novel Coronavirus, Infect. Dis. Poverty 9 (2020), 24. https://doi.org/10.1186/s40249-020-00640-3.
  6. M. Das, G.P. Samanta, Optimal Control of a Fractional Order Epidemic Model with Carriers, Int. J. Dyn. Control 10 (2022), 598–619. https://doi.org/10.1007/s40435-021-00822-3.
  7. M. Das, G. Samanta, Stability Analysis of a Fractional Ordered COVID-19 Model, Comput. Math. Biophys. 9 (2021), 22–45. https://doi.org/10.1515/cmb-2020-0116.
  8. K. Diethelm, N.J. Ford, A.D. Freed, A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations, Nonlinear Dyn. 29 (2002), 3–22. https://doi.org/10.1023/A:1016592219341.
  9. K. Diethelm, The Analysis of Fractional Differential Equations, Springer Berlin Heidelberg, 2010. https://doi.org/10.1007/978-3-642-14574-2.
  10. P. van den Driessche, J. Watmough, Reproduction Numbers and Sub-threshold Endemic Equilibria for Compartmental Models of Disease Transmission, Math. Biosci. 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6.
  11. G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, et al., Modelling the COVID-19 Epidemic and Implementation of Population-Wide Interventions in Italy, Nat. Med. 26 (2020), 855–860. https://doi.org/10.1038/s41591-020-0883-7.
  12. S. He, Y. Peng, K. Sun, SEIR Modeling of the COVID-19 and Its Dynamics, Nonlinear Dyn. 101 (2020), 1667–1680. https://doi.org/10.1007/s11071-020-05743-y.
  13. M.A. Khan, A. Atangana, Modeling the Dynamics of Novel Coronavirus (2019-nCov) with Fractional Derivative, Alexandria Eng. J. 59 (2020), 2379–2389. https://doi.org/10.1016/j.aej.2020.02.033.
  14. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, 2006.
  15. S. Lenhart, J.T. Workman, Optimal Control Applied to Biological Models, Chapman and Hall/CRC, 2007. https://doi.org/10.1201/9781420011418.
  16. Y. Luchko, Boundary Value Problems for the Generalized Time-Fractional Diffusion Equation of Distributed Order, Fract. Calc. Appl. Anal. 12 (2009), 409–422.
  17. F. Ndaïrou, I. Area, J.J. Nieto, D.F.M. Torres, Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan, Chaos Solitons Fractals 135 (2020), 109846. https://doi.org/10.1016/j.chaos.2020.109846.
  18. I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, Academic Press, 1999. https://doi.org/10.1016/s0076-5392(99)x8001-5.
  19. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience Publishers, 1962.
  20. M. Das, G. Samanta, M. De la Sen, A Fractional Ordered COVID-19 Model Incorporating Comorbidity and Vaccination, Mathematics 9 (2021), 2806. https://doi.org/10.3390/math9212806.
  21. N.H. Tuan, H. Mohammadi, S. Rezapour, A Mathematical Model for COVID-19 Transmission by Using the Caputo Fractional Derivative, Chaos Solitons Fractals 140 (2020), 110107. https://doi.org/10.1016/j.chaos.2020.110107.
  22. World Health Organization, WHO Director-General’s Opening Remarks at the Media Briefing on COVID-19 – 11 March 2020, 2020. https://www.who.int/news-room/speeches/item/who-director-general-s-opening-remarks-at-the-media-briefing-on-covid-19---11-march-2020.
  23. J.T. Wu, K. Leung, G.M. Leung, Nowcasting and Forecasting the Potential Domestic and International Spread of the 2019-nCoV Outbreak Originating in Wuhan, China: A Modelling Study, Lancet 395 (2020), 689–697. https://doi.org/10.1016/S0140-6736(20)30260-9.