A numerical investigation for the COVID-19 spatiotemporal lockdown-vaccination model

Document Type : Research Paper

Authors

1 Basic Science Department, Al-Safwa High Institute of Engineering, Egypt.

2 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.

3 Higher Technological Institute, Tenth of Ramadan City, Egypt.

Abstract

The present article investigates a numerical analysis of COVID-19 (temporal and spatio-tempora) lockdown-vaccination models. The proposed models consist of six nonlinear ordinary differential equations as a temporal model and six nonlinear partial differential equations as a spatio-temporal model. The evaluation of reproduction number is a forecast spread of the COVID-19 pandemic. Sensitivity analysis is used to emphasize the importance of pandemic parameters. We show the stability regions of the disease-free equilibrium point and pandemic equilibrium point. We use effective methods such as central finite difference (CFD) and Runge-Kutta of fifth order (RK-5). We apply Von-Neumann stability and consistency of the numerical scheme for the spatio-temporal model. We examine and compare the numerical results of the proposed models under various parameters.

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References

  • [1] A. R. Adem, T. S. Moretlo, and B. Muatjetjeja, A generalized dispersive water waves system: Conservation laws; symmetry reduction; travelling wave solutions; symbolic computation, Partial Differ Eqn Appl Math., 7(100465) (2022).
  • [2] P. Agarwal, M. A. Ramadan, A. A. M. Rageh, and A. R. Hadhoud, A fractional-order mathematical model for analyzing the pandemic trend of COVID-19, Math Meth Appl Sci., 45(8) (2022), 4625–4642.
  • [3] K. K. Ali, S. B. G. Karakoc, and H. Rezazadeh, Optical soliton solutions of the fractional perturbed nonlinear schrodinger equation, TWMS Journal of Applied and Engineering Mathematics, 10(4) (2020), 930–939.
  • [4] K. K. Ali, S. M. Mona, M. I. Abdelrahman, and M. A. Shaalan, Analytical and Numerical solutions for fourth order Lane-Emden-Fowler equation, Partial Differ Eqn Appl Math., 6(100430) (2022).
  • [5] O. A. Arqub and B. Maayah, Adaptive the Dirichlet model of mobile/immobile advection/dispersion in a timefractional sense with the reproducing kernel computational approach: Formulations and approximations, International Journal of Modern Physics B,37(18) (2350179) (2023).
  • [6] S. A. Baba, A. Yusuf, K. S. Nisar, A. Abdel-Aty, and T. A. Nofal, Mathematical model to assess the imposition of lockdown during COVID-19 pandemic, Result in Phys., 20(103716) (2021), 1–7.
  • [7] M. Banan and A. Omar, Hilbert approximate solutions and fractional geometric behaviors of a dynamical fractional model of social media addiction affirmed by the fractional Caputo differential operator, Chaos, Solitons & Fractals, 10(100092) (2023).
  • [8] M. Banan, A. Omar, A. Salam, and A. Hamed, Numerical solutions and geometric attractors of a fractional model of the cancer-immune based on the Atangana-Baleanu-Caputo derivative and the reproducing kernel scheme, Chinese Journal of Physics, 80 (2022), 463–483.
  • [9] S. K. Biswas, J. K. Ghosh, S. Sarkar, and U. Ghosh, COVID-19 pandemic in India: a mathematical model study, Non. Dyn., 102(1) (2020), 537–553.
  • [10] Y. Chayu and W. Jin, A mathematical model for the novel coronavirus epidemic in Wuhan, China Math biosc and eng., 17(3) (2020), 2708–2724.
  • [11] S. Djaouea, G. G. Kolayea, H. Abboubakar, A. A. Ari, and I. Damakoa, Mathematical modeling analysis and numerical simulation of the COVID-19 transmission with mitigation of control strategies used in Cameroon, Chaos, Solit & Fract., 139(110281) (2020), 1–15.
  • [12] A. Fatemeh, S. Manmohan, and R. David, Modelling of tumor cells regression in response to chemotherapeutic treatment, Appl Math Mode., 48(5) (2017), 96–112.
  • [13] S. B. G. Karakoc, K. K. Ali, and D. Y. Sucu, A new perspective for analytical and numerical soliton solutions of the Kaup−Kupershmidt and Ito equations, Journal of Computational and Applied Mathematics, 421(114850) (2023).
  • [14] A. F. Koura , K. R. Raslan, K. K. Ali, and M. A. Shaalan, Numerical analysis of a spatio-temporal bi modal coronavirus disease pandemic, Appl Math and Inf Sci., 16(5) (2022), 729–737.
  • [15] A. J. Kucharski, T. W. Russell, C. Diamond, Y. Liu, and J. Edmunds, Early dynamics of transmission and control of COVID-19: a mathematical modelling study, Inf Dise., 20(5) (2020), 553–558.
  • [16] B. Maayah, A. Moussaoui, S. Bushnaq, and O. A. Arqub, The multistep Laplace optimized decomposition method for solving fractional-order coronavirus disease model (COVID-19) via the Caputo fractional approach, Demonstratio Mathematica, 55(1) (2022), 963–977.
  • [17] M. Mandal, S. Jana, S. K. Nandi, A. Khatua, S. Adak, and T. K. Kar, A model based study on the dynamics of COVID-19, prediction and control, Chaos, Solit & Fract., 136(109889) (2020), 1–12.
  • [18] H. Mohammadi, S. Kumar, S. Rezapour, and S. Etemad, A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control, J of Chaos, Solit & Fract., 144(110668) (2021).
  • [19] R. P. Mondaini and P. M. Pardalos, Mathematical modelling of biosystems, Sprin Sci & Bus Media, 2008.
  • [20] C. Rothe, M. Schunk, P. Sothmann, G. Bretzel, G. Froeschl, C. Wallrauch, and et al., Transmission of 2019-nCoV infection from an asymptomatic contact in Germany, N Eng J of Med., 382(10) (2020), 970–971.
  • [21] N. H. Tuan, H. Mohammadi, and S. Rezapour, A mathematical model for COVID-19 transmission by using the Caputo fractional derivative, J. of Chaos, Solit. and Fract., 140(110107) (2020).
  • [22] J. A. M. Valle, Predicting the number of total COVID-19 cases and deaths in Brazil by the Gompertz model, Non. Dyn., 102(4) (2020), 2951–2957.
  • [23] D. Wrapp, N. Wang, K. S. Corbett, J. A. Goldsmith, C. Hsieh, O. Abiona, and et al., Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation, Science., (367)(6483) (2020), 1260–1263.
  • [24] Z. Zhang, A. Zeb, O. F. Egbelowo, and V. S. Erturk, Dynamics of a fractional order mathematical model for COVID-19 epidemic, Adv Differ Equ., 420 (2020), 1–16.
Computational Methods for Differential Equations
Volume 12, Issue 4
October 2024
Pages 669-686

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History

  • Receive Date: 12 June 2023
  • Revise Date: 20 February 2024
  • Accept Date: 27 March 2024

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