Numerical behavior of a fractional order dynamical model of RNA silencing

Simple item page
dc.AffiliationOctober University for modern sciences and Arts (MSA)
dc.contributor.authorEl-Sayed, AMA
dc.contributor.authorKhalil, M
dc.contributor.authorArafa, AAM
dc.contributor.authorSayed, Amaal
dc.date.accessioned2020-01-29T12:15:05Z
dc.date.available2020-01-29T12:15:05Z
dc.date.issued2016
dc.descriptionMSA Google Scholaren_US
dc.description.abstractA class of fractional-order differential models of RNA silencing with memory is presented in this paper. We also carry out a detailed analysis on the stability of equilibrium and we show that the model established in this paper possesses non-negative solutions. Numerical solutions are obtained using a predictor-corrector method to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. Numerical simulations are presented to illustrate the results. Also, the numerical simulations show that, modeling the phenomena of RNA silencing by fractional ordinary differential equations (FODE) has more advantages than classical integer-order modeling.en_US
dc.identifier.citation[1] E. Ahmed and A.S. Elgazzar,” On fractional order differential equations model for nonlocal epidemics”, PHYSICA A, 379 (2007) 607–614. http://dx.doi.org/10.1016/j.physa.2007.01.010. [2] E. Ahmed, A.M.A. El-Sayed, H.A.A. El-Saka,” Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models”, J. Math. Anal. Appl. 325 (2007) 542–553, http://dx.doi.org/10.1016/j.jmaa.2006.01.087. [3] F. Aini Abdullah and Ahmad Izani Md. Ismail, Simulations of the Spread of the Hantavirus Using Fractional Differential Equations, Matematika, 27(2011) 149-158. [4] A.A.M. Arafa, S.Z. Rida, M. Khalil,” Fractional modeling dynamics of HIV and CD4+ T-cells during primary infection”, Nonlinear Biomedical Physics 6(2012) 1-7, http://dx.doi.org/10.1186/1753- 4631-6-1. [5] A.A.M. Arafa, S.Z. Rida, M. Khalil,” The effect of anti-viral drug treatment of human immunodeficiency”, Appl. Math. Model, 37 (2013) 2189–2196,http://dx. doi:10.1016/j.apm.2012.05.002 http://dx.doi.org/10.1016/j.apm.2012.05.002. [6] A.A.M. Arafa, S.Z. Rida. M. Khalil,” Solutions of Fractional model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells using HAM”, International Journal of Basic and Applied Sciences, 1 (1) (2012) 1-14. http://dx.doi.org/10.14419/ijbas.v1i1.15. [7] D. Baulcombe, “RNA silencing”, Curr. Biol. 12, (2002) R82–R84, http://dx.doi.org/10.1016/S0960-9822(02)00665-6.. [8] C.T. Bergstrom, E. McKittrick, R. Antia,” Mathematical models of RNA silencing: Unidirectional amplification limits accidental selfdirected reactions”, PNAS, 100 (2003) 11511–11516. http://dx.doi.org/10.1073/pnas.1931639100. [9] M. Dalir, M. Bashour,” Applications of Fractional Calculus”, Appl. Math. Sci. 4 (2010) 1021–1032. [10] E. Demirci, Arzu Unal and Nuri Ozalp,” A fractional order SEIR Model with density dependent death rate”, Hacet. J. Math. Stat., 40 (2) (2011) 287 – 295. [11] W. Deng,” Smoothness and stability of the solutions for nonlinear fractional differential equations”, Nonlinear Anal-Theor. 72 (2010) 1768-1777, http://dx.doi.org/10.1016/j.na.2009.09.018. [12] K. Diethelm,” The Analysis of Fractional Differential Equations”, Springer-Verlag, Berlin, (2010) 181-182. [13] Y. Ding, H. Yea,” A fractional-order differential equation model of HIV infection of CD4+T-cells”, Math. Comput. Model. 50 (2009) 386–392, http://dx.doi.org/10.1186/1753-4631-6-1. [14] A. Eamens, M.B. Wang, N. A. Smith, P. M. Waterhouse,” RNA Silencing in Plants: Yesterday, Today, and Tomorrow”, Plant Physiology,147(2008),456–468, http://dx.doi.org/10.1104/pp.108.117275. [15] A.E.M. El-Misiery, E. Ahmed,” On a fractional model for earthquakes”, Appl. Comput. Math. 178 (2006) 207–211. http://dx.doi.org/10.1016/j.amc.2005.10.011. [16] A.M.A. El-Sayed, I.L. El-Kalla, E.A.A. Ziada,” Analytical and numerical solutions of multi-term nonlinear fractional orders differential equations”, Applied Numerical Mathematics 60 (2010) 788– 797, http://dx.doi.org/10.1016/j.apnum.2010.02.007. [17] A.M.A. El-Sayed, M.E. Nasr,” Existence of uniformly stable solutions of non-autonomous discontinuous dynamical systems”, J.Egyptian Math. Soc. (2011) 19, 91-94. http://dx.doi.org/10.1016/j.joems.2011.09.006. [18] A.M.A. El-Sayed,” On the existence and stability of positive solution for a nonlinear fractional-order differential equation and some applications”, Alex. J. Math. 1 (2010) 1–10. [19] A.M.A. El-Sayed, S.Z. Rida, A.A.M. Arafa,” Exact solutions of some time-fractional biological population models by using generalized differential transform method”, Int. J. Math. Model. Simul. Appl. 3 (2010) 231–239. [20] A.M.A. El-Sayed, S.Z. Rida, A.A.M. Arafa,” On the Solutions of Time-fractional Bacterial Chemotaxis in a Diffusion Gradient Chamber”, Int. J. Nonlinear Sci. Numer., 7(2009) 485–492. [21] A.M.A. El-Sayed, A. E. M. El-Mesiry, and H. A. A. El-Saka,” Numerical solution for multi-term fractional (arbitrary) orders differential equations”, Comput. Appl. Math., 23(2004)33–54. http://dx.doi.org/10.1590/S0101-82052004000100002. [22] M.A.C. Groenenboom, P. Hogeweg,” Modelling the dynamics of viral suppressors of RNA silencing”, J. R. Soc. Interface 9(2012), 436–447. http://dx.doi.org/10.1098/rsif.2011.0361. [23] C.P. Li and F.R. Zhang,” A survey on the stability of fractional differential equations”, Eur. Phys. J. Special Topics 193 (2011) 27–47. http://dx.doi.org/10.1140/epjst/e2011-01379-1.[24] W. Lin,” Global existence theory and chaos control of fractio nal differential equations”, J. Math. Anal. Appl. 332 (2007) 709 –726, http://dx.doi.org/10.1016/j.jmaa.2006.10.040 . [25] S. Mlotshwa, O. Voinnet, M. Florian Mette, M. Matzke, H. Vaucheret, S. Wei Ding, G. Pruss, V. B. Vance, “RNA Silencing and the Mobile Silencing Signal”, The Plant Cell, (2002) 289 – 301,http://dx. doi: 10.1105/tpc.001677. [26] S. Nikolov,” Dynamics and Complexity in a Time Delay Mo del of RNA Silencing with Periodic Forcing”, Bioautomation, 10(2008) 1 - 12. [27] Z. Odibat and N. Shawagfeh,” Generalized Taylor’s formula”, Appl. Math. Comput. 186 (2007) 286 –293, http://dx.doi.org/10.1155/2015/507970 . [28] Z. Odibat, and Shaher Moamni,” An algorithm for the numer i cal solution of differential equations of fractional order”, J. Appl. Math. & Informatics, 26(2008) 15 – 27. [29] L.M. Petrovic, D.T. Spasic, T.M. Atanackovic,” On a math ematical model of a human root dentin”, Dental Materials, 21(2005), 125 - 128. http://dx.doi.org/10.1016/j.dental.2004.01.004 . [30] S. Pfeffer, G. Meister, M. Landthaler, T. Tuschl,” RNA silen cing”, B.I.F. Futura, 20 (2005). [31] F.A. Rihan,” Numerical Modeling of Fractional -Order Biolog ical Systems”, Abstract and Applied Analysis, 2013, http://dx.doi.org/10.1155/2013/816803 . [32] V. Suat Ertürk, Zaid M. Odibat, Shaher Momani,” An appro ximate solution of a fractional order differential equation model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+T-cells”, Computers and Mathematics with Applications 62 (2011) 996 – 1002. http://dx.doi.org/10.1016/j.camwa.2011.03.091 . [33] What is RNA? : http://www.umassmed.edu/rti/biology/rna -faq/ [34] Why is RNA important to the cell?: https://www.reference.com/science/rna -important -cell - bcdd937bd3cbc9b3.en_US
dc.identifier.doihttps://doi.org/10.14419/ijsw.v4i2.6474
dc.identifier.otherhttps://doi.org/10.14419/ijsw.v4i2.6474
dc.identifier.urihttps://t.ly/1MGeB
dc.language.isoenen_US
dc.publisherInternational Journal of Scientific Worlden_US
dc.relation.ispartofseriesnternational Journal of Scientific World;4 (2) (2016) 52-56
dc.subjectFractional Calculusen_US
dc.subjectRNA Silencing Fractional Order Modelen_US
dc.subjectPredictor-Corrector Methoden_US
dc.titleNumerical behavior of a fractional order dynamical model of RNA silencingen_US
dc.typeArticleen_US

Files

Original bundle

Now showing 1 - 2 of 2
Thumbnail Image
Name:
avatar_scholar_256.png
Size:
6.31 KB
Format:
Portable Network Graphics
Description:
Faculty Of Engineering Research Paper
Download
Thumbnail Image
Name:
document.pdf
Size:
517.91 KB
Format:
Adobe Portable Document Format
Description:
Download

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
51 B
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Faculty Of Engineering Research Paper