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Journals / Turkish Journal of Science / 2026 / Cilt: 5 Sayı: 2

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

İlknur Koca(BURDUR MEHMET AKİF ERSOY ÜNİVERSİTESİ)
Eyüp Akçetin(Muğla Sıtkı Koçman University)
Pelin Yaprakdal(BURDUR MEHMET AKİF ERSOY ÜNİVERSİTESİ)
Pages
124–139
Publication Date
2020-10-31
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, the efficient numerical method for finding solutions of system is given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In our paper, the spread of SIQR model with fractional order differential equation is considered.
📊
Key Findings & Data:We have evaluated the system with fractional way and investigated stability of the non-virus equilibrium point and virus equilibrium points.
💡
Conclusion & Impact:Finally, the efficient numerical method for finding solutions of system is given.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Fractional order differential equations · stability · Caputo 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.

🔖

Cite This Article

Koca, İ., Akçetin, E., Yaprakdal, P. (2020). Numerical Approximation for the Spread of SIQR Model with Caputo Fractional Order Derivative. Turkish Journal of Science, Cilt: 5 Sayı: 2, 124–139. https://ajindex.com/articles/1557568

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References (38)

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  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)
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  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
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  14. Petráš, I. (2011). Fractional-order nonlinear systems: modeling, analysis and simulation. Springer Science & Business Media
  15. Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Vol
  16. 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
  20. 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
  21. Atangana, A., & Koca, I. (2016). On the new fractional derivative and application to nonlinear Baggs and Freedman model. J. Nonlinear Sci. Appl, 9(5)
  22. Baskonus HM, Mekkaoui T, Hammouch H, et al. Active control of a Chaotic fractional order economic system. Entropy 2015; 17: 5771--5783.3413-3442
  23. Benson, D. A., Wheatcraft, S. W., & Meerschaert, M. M. (2000). Application of a fractional advection-dispersion equation. Water resources research, 36(6), 1403-1412
  24. 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
  25. 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
  26. Debnath, L. (2004). A brief historical introduction to fractional calculus. International Journal of Mathematical Education in Science and Technology, 35(4), 487-501
  27. Diethelm, K. (2010). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. Springer Science & Business Media
  28. Koca, I. (2018). Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators. The European Physical Journal Plus, 133(3), 100
  29. Linda J.S. Allen, "An Introduction to mathematical biology," Pearson/Prentice Hall, (2007)
  30. 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
  31. Mu, Y., Li, Z., Xiang, H., & Wang, H. (2017). Bifurcation analysis of a turbidostat model with distributed delay. Nonlinear Dynamics, 90(2), 1315-1334
  32. 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
  33. Petráš, I. (2011). Fractional-order nonlinear systems: modeling, analysis and simulation. Springer Science & Business Media
  34. Podlubny, I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Vol
  35. Elsevier, 1998
  36. 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
  37. 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
  38. 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.