Araştırma Makalesi
Yıl 2020,
Cilt: 5 Sayı: 2, 124 - 139, 31.10.2020
Öz
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.
Anahtar Kelimeler
Fractional order differential equations stability Caputo derivative,
Kaynakça
- [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.
Yıl 2020,
Cilt: 5 Sayı: 2, 124 - 139, 31.10.2020
Öz
Kaynakça
- [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.
Toplam 1 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Volume V Issue II 2020 |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Ekim 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 5 Sayı: 2 |
