An efficient numerical algorithm for solving fractional SIRC model with salmonella bacterial infection

Rubayyi T. Alqahtani; M. A. Abdelkawy; Rubayyi T. Alqahtani; M. A. Abdelkawy

doi:10.3934/mbe.2020212

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 4: 3784-3793. doi: 10.3934/mbe.2020212

Previous Article Next Article

Research article Special Issues

An efficient numerical algorithm for solving fractional SIRC model with salmonella bacterial infection

Rubayyi T. Alqahtani ¹,
M. A. Abdelkawy ^{1,2
,
,}

1.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11564, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt

Received: 26 March 2020 Accepted: 11 May 2020 Published: 25 May 2020

This paper revisits the study of numerical approaches for fractional SIRC model with Salmonella bacterial infection (FSIRC-MSBI). This model is investigated by the aid of fully shifted Jacobi's collocation method for temporal discretization. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.
- fractional SIRC model,
- spectral collocation method,
- Gauss-Radau quadrature,
- Shifted Jacobi polynomials,
- Caputo fractional derivative
Citation: Rubayyi T. Alqahtani, M. A. Abdelkawy. An efficient numerical algorithm for solving fractional SIRC model with salmonella bacterial infection[J]. Mathematical Biosciences and Engineering, 2020, 17(4): 3784-3793. doi: 10.3934/mbe.2020212

Related Papers:

Abstract

This paper revisits the study of numerical approaches for fractional SIRC model with Salmonella bacterial infection (FSIRC-MSBI). This model is investigated by the aid of fully shifted Jacobi's collocation method for temporal discretization. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.

References

[1]	M. Al-Smadi, O. A. Arqub, Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates, Appl. Math. Comput., 342 (2019), 280-294.
[2]	S. Qureshi, A. Yusuf, Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator, Chaos Solitons Fractals, 126 (2019), 32-40. doi: 10.1016/j.chaos.2019.05.037
[3]	E. Bas, B. Acay, The direct spectral problem via local derivative including truncated Mittag-Leffler function, Appl. Math. Comput., 367 (2020), 124787.
[4]	B. Acay, E. Bas, T. Abdeljawad, Non-local fractional calculus from different viewpoint generated by truncated M-derivative, J. Comput. Appl. Math., 366 (2020), 112410. doi: 10.1016/j.cam.2019.112410
[5]	B. Acay, E. Bas, T. Abdeljawad, Fractional economic models based on market equilibrium in the frame of different type kernels, Chaos Solitons Fractals, 130 (2020), 109438. doi: 10.1016/j.chaos.2019.109438
[6]	F. Songa, C. Xu, Spectral direction splitting methods for two-dimensional space fractional diffusion equations, J. Comput. phys., 299 (2015), 196-214. doi: 10.1016/j.jcp.2015.07.011
[7]	S. Qureshi, A. Yusuf, Fractional derivatives applied to MSEIR problems: Comparative study with real world data, Eur. Phys. J. Plus, 134 (2019), 171. doi: 10.1140/epjp/i2019-12661-7
[8]	A. A. Al-nana, O. A. Arqub, M. Al-Smadi, N. Shawagfeh, Fitted spectral Tau Jacobi technique for solving certain classes of fractional differential equations, Appl. Math, 13 (2019) 979-987.
[9]	S. Qureshi, A. Yusuf, Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu, Chaos Solitons Fractals, 122 (2019), 111-118. doi: 10.1016/j.chaos.2019.03.020
[10]	R. Mollapourasl, A. Ostadi, On solution of functional integral equation of fractional order, Appl. Math. Comput., 270 (2015), 631-643.
[11]	X. Shu, F. Xub, Y. Shi, S-asymptotically ω-positive periodic solutions for a class of neutral fractional differential equations, Appl. Math. Comput., 270 (2015), 768-776.
[12]	N. Sahin, S. Yuzbasi, M. Gulsu, A collocation approach for solving systems of linear Volterra integral equations with variable coefficients, Comput. Math. Appl., 62 (2011), 755-769. doi: 10.1016/j.camwa.2011.05.057
[13]	W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proc. R. Soc. London, 115 (1927), 700-721.
[14]	A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission, Bull. Math. Biol., 68 (2006), 615-626. doi: 10.1007/s11538-005-9037-9
[15]	Y. Cha, Stability change of an epidemic model, Dyn. Syst. Appl., 9 (2000), 361-376.
[16]	R. Casagrandi, L. Bolzoni, S. A. Levin, V. Andreasen, The SIRC model and influenza A, Math. Biosci., 200 (2006), 152-169. doi: 10.1016/j.mbs.2005.12.029
[17]	S. Hasan, A. Al-Zoubi, A. Freihet, M. Al-Smadi, S. Momani, Solution of fractional SIR epidemic model using residual power series method, Appl. Math. Inf. Sci., 13 (2019), 1-9. doi: 10.18576/amis/13S101
[18]	S. Hasan, A. El-Ajou, S. Hadid, M. Al-Smadi, S. Momani, Atangana-Baleanu fractional framework of reproducing kernel technique in solving fractional population dynamics system, Chaos Solitons Fractals, 133 (2020), 109624. doi: 10.1016/j.chaos.2020.109624
[19]	M. El-Shahed, A. Alsaedi, The fractional SIRC model and influenza A, Math. Probl. Eng., 2011 (2011).
[20]	M. A. Abdelkawy, A. M. Lopes, Mohammed M. Babatin, Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order, Chaos Solitons Fractals, 134 (2020), 109721. doi: 10.1016/j.chaos.2020.109721
[21]	E. L. Ortiz, H. J. Samara, An operational approach to the Tau method for the numerical solution of non-linear differential equations, Computing, 27 (1981), 15-25. doi: 10.1007/BF02243435
[22]	R. M. Hafez, M. A. Zaky, M. A. Abdelkawy, Jacobi Spectral Galerkin method for Distributed-Order Fractional Rayleigh-Stokes problem for a Generalized Second Grade Fluid, Front. Phys., 7 (2020).
[23]	E. H. Doha, A. H. Bhrawy, R. H. Hafez, A Jacobi dual-Petrov-Galerkin method for solving some odd-order ordinary differential equations, in Abstract and Applied Analysis, Hindawi, (2011).
[24]	G. Szegö, Orthogonal Polynomials, American Mathematical Society, (1939).
[25]	R. Beals, R. Wong, Special Functions: A graduate text, Cambridge University Press, (2010).
[26]	K. Miller, B. Ross, An Introduction to the Fractional Calaulus and Fractional Differential Equations, John Wiley & Sons Inc., (1993).
[27]	D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204 (1996), 609-625. doi: 10.1006/jmaa.1996.0456
[28]	Z. M. Odibat, Na.T. Shawagfeh, Generalized Taylor's formula, Appl. Math. Comput., 186 (2007), 286-293.
[29]	F. A. Rihan, D. Baleanu, S. Lakshmanan, R. Rakkiyappan, On fractional SIRC model with salmonella bacterial infection, in Abstract and Applied Analysis, Hindawi, (2011).
[30]	M. A. Abdelkawy, An improved collocation technique for distributed-order fractional partial differential equations, Rom. Rep. Phys., 72 (2020).
[31]	Y. G. Sanchez, Z. Sabir, J. L.G. Guirao, Design of a nonlinear SITR fractal model based on the dynamics of a novel coronavirus (COVID-19), Fractals, 2020 (2020).

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)