Research Article

Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative

Volume: 5 Number: 2 October 31, 2020
EN

Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative

Abstract

In our paper, the spread of SIQR model with fractional order differential equation is considered. We have evaluated the system with fractional way and investigated stability of the non-virus equilibrium point and virus equilibrium points. Also, the existence of the solutions are proved. Finally, the efficient numerical method for finding solutions of system is given.

In our paper, the spread of SIQR model with fractional order differential equation is considered. We have evaluated the system with fractional way and investigated stability of the non-virus equilibrium point and virus equilibrium points. Also, the existence of the solutions are proved. Finally, the efficient numerical method for finding solutions of system is given.

Keywords

References

  1. [1] Alkahtani, B. S. T., Atangana, A., & Koca, I. (2017). Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators. J. Nonlinear Sci. Appl, 10(6), 3191-3200. [2] Atangana, A., & Koca, I. (2016). On the new fractional derivative and application to nonlinear Baggs and Freedman model. J. Nonlinear Sci. Appl, 9(5). [3] Baskonus HM, Mekkaoui T, Hammouch H, et al. Active control of a Chaotic fractional order economic system. Entropy 2015; 17: 5771--5783.3413-3442. [4] Benson, D. A., Wheatcraft, S. W., & Meerschaert, M. M. (2000). Application of a fractional advection-dispersion equation. Water resources research, 36(6), 1403-1412. [5] Bulut H, Baskonus HM and Belgacem FBM. The analytical solutions of some fractional ordinary differential equations by Sumudu transform method. Abstr Appl Anal 2013; 2013: 203875-1--203875-6. [6] Debnath, L. (2003). Recent applications of fractional calculus to science and engineering. International Journal of Mathematics and Mathematical Sciences, 2003(54), feron-α therapy. Science, 282(5386), 103-107. [7] Debnath, L. (2004). A brief historical introduction to fractional calculus. International Journal of Mathematical Education in Science and Technology, 35(4), 487-501. [8] Diethelm, K. (2010). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. Springer Science & Business Media. [9] Koca, I. (2018). Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators. The European Physical Journal Plus, 133(3), 100. [10] Linda J.S. Allen, "An Introduction to mathematical biology," Pearson/Prentice Hall, (2007). [11] Liu, Q., Jiang, D., & Shi, N. (2018). Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching. Applied Mathematics and Computation, 316, 310-325. [12] Mu, Y., Li, Z., Xiang, H., & Wang, H. (2017). Bifurcation analysis of a turbidostat model with distributed delay. Nonlinear Dynamics, 90(2), 1315-1334. [13] Neumann, A. U., Lam, N. P., Dahari, H., Gretch, D. R., Wiley, T. E., Layden, T. J., & Perelson, A. S. (1998). Hepatitis C viral dynamics in vivo and the antiviral efficacy of inter [14] Odibat, Z. M. , Momani, S. (2006). Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Sciences and Numerical Simulation, 7(1), 27-34. [15] Petráš, I. (2011). Fractional-order nonlinear systems: modeling, analysis and simulation. Springer Science & Business Media. [16] Podlubny, I.. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Vol. 198. Elsevier, 1998. [17] Ross, B. (1975). A brief history and exposition of the fundamental theory of fractional calculus. In Fractional calculus and its applications (pp. 1-36). Springer, Berlin, Heidelberg. [18] Toufik, M., & Atangana, A. (2017). New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models. The European Physical Journal Plus, 132(10), 444. [19] Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences, 180(1-2), 29-48.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

October 31, 2020

Submission Date

June 8, 2020

Acceptance Date

October 30, 2020

Published in Issue

Year 2020 Volume: 5 Number: 2

APA
Koca, İ., Akçetin, E., & Yaprakdal, P. (2020). Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative. Turkish Journal of Science, 5(2), 124-139. https://izlik.org/JA52JS68BP
AMA
1.Koca İ, Akçetin E, Yaprakdal P. Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative. TJOS. 2020;5(2):124-139. https://izlik.org/JA52JS68BP
Chicago
Koca, İlknur, Eyüp Akçetin, and Pelin Yaprakdal. 2020. “Numerical Approximation for the Spread of SIQR Model With Caputo Fractional Order Derivative”. Turkish Journal of Science 5 (2): 124-39. https://izlik.org/JA52JS68BP.
EndNote
Koca İ, Akçetin E, Yaprakdal P (October 1, 2020) Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative. Turkish Journal of Science 5 2 124–139.
IEEE
[1]İ. Koca, E. Akçetin, and P. Yaprakdal, “Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative”, TJOS, vol. 5, no. 2, pp. 124–139, Oct. 2020, [Online]. Available: https://izlik.org/JA52JS68BP
ISNAD
Koca, İlknur - Akçetin, Eyüp - Yaprakdal, Pelin. “Numerical Approximation for the Spread of SIQR Model With Caputo Fractional Order Derivative”. Turkish Journal of Science 5/2 (October 1, 2020): 124-139. https://izlik.org/JA52JS68BP.
JAMA
1.Koca İ, Akçetin E, Yaprakdal P. Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative. TJOS. 2020;5:124–139.
MLA
Koca, İlknur, et al. “Numerical Approximation for the Spread of SIQR Model With Caputo Fractional Order Derivative”. Turkish Journal of Science, vol. 5, no. 2, Oct. 2020, pp. 124-39, https://izlik.org/JA52JS68BP.
Vancouver
1.İlknur Koca, Eyüp Akçetin, Pelin Yaprakdal. Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative. TJOS [Internet]. 2020 Oct. 1;5(2):124-39. Available from: https://izlik.org/JA52JS68BP