Modeling and simulation of COVID-19 disease dynamics via Caputo-Fabrizio fractional derivative

Document Type : Research Paper

Authors

1 Department of Mathematics, Malaviya National Institute of Technology Jaipur, India.

2 1. Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India. 2. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon.

Abstract

The motive of this paper is to investigate the SEIQRD model of the COVID-19 outbreak in Indonesia with the help of a fractional modeling approach. The model is described by the nonlinear system of six fractional order differential equations (DE) incorporating the Caputo-Fabrizio Fractional derivative (CFFD) operator. The existence and uniqueness of the model are proved by applying the well-known Banach contraction theorem. The reproduction number ($R_0$) is calculated, and its sensitivity analysis is conducted concerning each parameter of the model for the prediction and persistence of the infection. Moreover, the numerical simulation for various fractional orders is performed using the Adams-Bashforth technique to analyze the transmission behavior of disease and to get the approximated solutions. At last, we represent our numerical simulation graphically to illustrate our analytical findings.

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Main Subjects

References

  • [1] S. S. Alzaid and B. S. T. Alkahtani, On study of fractional order epidemic model of COVID-19 under non-singular Mittag-Leffler kernel, Results in Physics, 26 (2021), 104402.
  • [2] J. K. K. Asamoah, E. Okyere, E. Yankson, A. A. Opoku, A. A. Konadu, E. Acheampong, and Y. D. Arthur, Non-fractional and fractional mathematical analysis and simulations for Q fever, Chaos, Solitons & Fractals, 156 (2022), 111821.
  • [3] M. Aychluh, S. D. Purohit, P. Agarwal, and D. L. Suthar, AtanganaBaleanu derivative-based fractional model of COVID-19 dynamics in Ethiopia, Applied Mathematics in Science and Engineering, 30(1) (2022), 634-659.
  • [4] I. A. Baba and B. A. Nasidi, Fractional order epidemic model for the dynamics of novel COVID-19, Alexandria Engineering Journal, 60(1) (2021), 537-548.
  • [5] T. A. Biala and A. Q. M. Khaliq, A fractional-order compartmental model for the spread of the COVID-19 pandemic, Communications in Nonlinear Science and Numerical Simulation, 98 (2021), 105764.
  • [6] A. Cartocci, G. Cevenini, and P. Barbini, A compartment modeling approach to reconstruct and analyze gender and age-grouped CoViD-19 Italian data for decision-making strategies, Journal of Biomedical Informatics, 118 (2021), 103793.
  • [7] I. Cooper, A. Mondal, and C. G. Antonopoulos, A SIR model assumption for the spread of COVID-19 in different communities, Chaos, Solitons & Fractals, 139 (2020), 110057.
  • [8] I. Darti, M. Rayungsari, R. R. Musafir and A. Suryanto, A SEIQRD epidemic model to study the dynamics of COVID-19 disease, Communications in Mathematical Biology and Neuroscience, 2023 (2023), 5.
  • [9] M. A. Dokuyucu, E. Celik, H. Bulut, and H. M. Baskonus, Cancer treatment model with the Caputo-Fabrizio fractional derivative, The European Physical Journal Plus, 133 (2018), 1-6.
  • [10] M. Farman, H. Besbes, K. S. Nisar, and M. Omri, Analysis and dynamical transmission of Covid-19 model by using Caputo-Fabrizio derivative, Alexandria Engineering Journal, 66(1) (2023), 597-606.
  • [11] Z. Y. He, A. Abbes, H. Jahanshahi, N. D. Alotaibi and Ye Wang, Fractional-order discrete-time SIR epidemic model with vaccination, Chaos and complexity, 10(2) (2022), 165.
  • [12] H. Jafari, R. M. Ganji, N. S. Nkomo, and Y. P. Lv, A numerical study of fractional order population dynamics model, Results in Physics, 27 (2021), 104456.
  • [13] A. A. Khan, A. Alam, R. Amin, S. Ullah, W. Sumelka, and M. Altanji, Numerical simulation of a Caputo fractional epidemic model for the novel coronavirus with the impact of environmental transmission, Alexandria Engineering Journal, 61(7) (2022), 5083-5095.
  • [14] P. Kumar, V. S. Erturk, V. Govindaraj, M. Inc, H. Abboubakar, and K. S. Nisar ,Dynamics of COVID-19 epidemic via two different fractional derivatives, International Journal of Modeling, Simulation, and Scientific Computing, 14(3) (2023), 2350007.
  • [15] S. Kumawat, S. Bhatter, D. L. Suthar, S. D. Purohit, and K. Jangid, Numerical modeling on age-based study of coronavirus transmission, Applied Mathematics in Science and Engineering, 30(1) (2022), 609-634.
  • [16] K. Logeswari, C. Ravichandra, and K. S. Nisar, Mathematical model for spreading of COVID19 virus with the MittagLeffler kernel, Numerical Methods for Partial Differential Equations, 40(1) (2024), e22652.
  • [17] L. L´opez and X. Rodo, A modified SEIR model to predict the COVID-19 outbreak in Spain and Italy simulating control scenarios and multi-scale epidemics, Results in Physics, 21 (2021), 103746.
  • [18] M. Nehme, O. Braillard, G. Alcoba, S. A. Perone, D. Courvoisier, F. Chappuis, I. Guessous, and COVICARE TEAM†, COVID-19 symptoms: longitudinal evolution and persistence in outpatient settings, Annals of Internal Medicine, 174(5) (2021), 723-725.
  • [19] K. S. Nisar, M. Farman, M. A. Aty, and J. Cao, Mathematical Epidemiology: A Review of the Singular and NonSingular Kernels and their Applications, Progress in Fractional Differentiation and Applications, 9(4) (2023), 507-544.
  • [20] M. M. Ojo, O. J. Peter, E. F. D. Goufo, and K. S. Nisar, A mathematical model for the co-dynamics of COVID-19 and tuberculosis, Mathematics and Computers in Simulation, 207 (2023), 499-520.
  • [21] W. Pan, T. Li, and S. Ali ,A fractional order epidemic model for the simulation of outbreaks of Ebola, Advances in Difference Equations, 2021 (2021), 161.
  • [22] L. Peng, W. Yang, D. Zhang, C. Zhuge, and L. Hong Epidemic analysis of COVID-19 in China by dynamical modeling, arXiv preprint, 2002 (2020), 06563.
  • [23] K. Rajagopal, N. Hasanzadeh, F. Parastesh, I. I. Hamarash, S. Jafari, and I. Hussain, A fractional-order model for the novel coronavirus (COVID-19) outbreak, Nonlinear Dynamics, 101 (2020), 711-718.
  • [24] S. Rezapour, H. Mohammadi, and M. E. Samei, SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order, Advances in difference equations, 2020 (2020), 490.
  • [25] Shyamsunder, S. Bhatter, K. Jangid, A. Abidemi, K. M. Owolabi, and S. D. Purohit, A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks, Decision Analytics Journal, 6 (2023), 100156.
  • [26] K. Shah, F. Jarad, and T. Abdeljawad, On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative, Alexandria Engineering Journal, 59(4) (2020), 2305-2313.
  • [27] P. Verma and M. Kumar, Analysis of a novel coronavirus (2019-nCOV) system with variable Caputo-Fabrizio fractional order, Chaos, Solitons & Fractals, 142 (2021), 110451.
  • [28] S. W. Yao, M. Farman, A. Akgul, K. S. Nisar, M. Amin, M. U. Saleem, and M. Inc, Simulations and analysis of Covid-19 as a fractional model with different kernels, Fractals, 31(4) (2023), 2340051.
  • [29] A. Zeb, E. Alzahrani, V. S. Erturk, and G. Zaman, Mathematical model for coronavirus disease 2019 (COVID-19) containing isolati

 

 

Computational Methods for Differential Equations
Volume 13, Issue 2
March 2025
Pages 494-504

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History

  • Receive Date: 12 December 2023
  • Revise Date: 30 March 2024
  • Accept Date: 21 April 2024

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