Article ID: MTJPAM-D-21-00027

Title: Mathematical Modelling of COVID-19 Using Approximated Hyper-Singular Integral Based Chebyshev Polynomials of the Second Kind


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00027; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 33-40

Document Type: Research Paper

Author(s): Suzan J. Obaiys a , Teng Wen Ni b , Joshua Yim Wei Xiang c , Rabha W. Ibrahim d

aSchool of Mathematical and Computer Sciences, Heriot-Watt University, Malaysia

bSchool of Mathematical and Computer Sciences, Heriot-Watt University, Malaysia

cSchool of Mathematical and Computer Sciences, Heriot-Watt University, Malaysia

dIEEE: 94086547, Kuala Lumpur, 59200, Malaysia

Received: 7 April 2021, Accepted: 23 June 2021, Published: 16 July 2021.

Corresponding Author: Suzan J. Obaiys (Email address: s.obaiys@hw.ac.uk)

Full Text: PDF

Abstract

There are different investigations unfilled the population energetic of COVID-19. In this work, we formulate an approximated hypersingular integral based Chebyshev polynomials of second kind to simulate COVID-19 growth. The planned scheme indicates an association consequences of integral equation model by employing live data from Malaysia for three different months. MATLAB code is developed to obtain the numerical results for the presented problem. Moreover, the error function is applied to determine the compact interval of the infected number. We could establish agreement action on the displays where the numerical results assert the theoretical concept.

Keywords: Singular integrals, Hypersingular integral, Chebyshev polynomial, COVID-19

References:
  1. R. L. Burden and J. Faires, Numerical analysis. Seventh Edition, Brooks/Cole Pub. 2001.
  2. V. J. Ervin and E. P. Stephan, Collocation with Chebyshev polynomials for a hypersingular integral equation on an interval. Journal of Computational and Applied Mathematics 43 (1-2), 221–229, 1992.
  3. S. B. Hadid, W. I. Rabha, D. Altulea and S. Momani, Solvability and stability of a fractional dynamical system of the growth of COVID-19 with approximate solution by fractional Chebyshev polynomials. Advances in Difference Equations 2020 (1), 1–16, 2020.
  4. R. W. Ibrahim, D. Altulea and R. M. Elobaid, Dynamical system of the growth of COVID-19 with controller. Advances in Difference Equations 2021 (1), 1–12, 2021.
  5. E. Jiang, F. Zhao and Y. Shu, Numerical approximation. Fudan University Press, Shanghai, 2008.
  6. S. J. Obaiys, Z. K. Eshkuvatov and N. M. A. Nik Long On error estimation of automatic quadrature scheme for the evaluation of Hadamard integral of second order singularity. University of Bucharest. Scientific Bulletin. Series A. Applied Mathematics and Physics 75 (1), 85–98, 2013.
  7. S. J. Obaiys, On the convergence problem of one-dimensional hypersingular integral equations. Mathematical Problems in Engineering 2013, 2013; Article ID 974751.
  8. S. J. Obaiys, Z. Abbas, N. M. A. Nik Long, A. F. Ahmad, A. Ahmedov and H. K. Raad, On the general solution of first-kind hypersingular integral equations. Am. J. Eng. Applied Sci 9 195–201, 2016.
  9. S. J. Obaiys, R. W. Ibrahim and A. F. Ahmad, Hypersingular integrals in integral equations and inequalities: fundamental review study. Differential and Integral Inequalities 687–717, 2019.
  10. M. A. Khan and A. Atangana. Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alexandria Engineering Journal 59 (4), 2379–2389, 2020.
  11. D. Lanteri, D. Carco and P. Castorina. How macroscopic laws describe complex dynamics: asymptomatic population and CoviD-19 spreading. arXiv preprint arXiv:2003.12457, 2020.
  12. J. Mason and D. Handscomb, Chebyshev polynomials. CRC Prress LLC, 2003.
  13. A. M. Mishra, S. D. Purohit, K. M. Owolabi and Y. D. Sharma, A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus. Chaos, Solitons & Fractals, 109953, 2020.
  14. S. Momani, R. W. Ibrahim and S. B. Hadid. Susceptible-infected-susceptible epidemic discrete dynamic system based on tsallis entropy. Entropy 22 (7), 769, 2020.
  15. World Health Organization, Coronavirus disease (COVID-19) outbreak, https://www.who.int/emergencies/diseases/novel-coronavirus-2019.
  16. World Health Organization, Coronavirus disease (COVID-19) report, https://www.who.int/docs/default-source/coronaviruse/who-china-joint-mission-on-covid-19-final-report.pdf.