ADOMIAN’S METHOD FOR SOLVING A NONLINEAR EPIDEMIC MODEL
Keywords:
ordinary differential equation, pandemic, initial value problem, series solution, Padé, exact solutionDOI:
https://doi.org/10.17654/0974324324006Abstract
This paper solves the susceptible-infected-recovered (SIR) model by means of the Adomian decomposition method (ADM). The ADM provides series solutions for the infected and recovered individuals. Such series solutions transform to exact ones under certain constraints of the initial conditions. In addition, closed form solutions are obtained for the infected and recovered individuals by rearranging the components of the ADM series. The accuracy is examined via comparing our results with an accurate numerical method. Agreement between our results and those of the numerical method is achieved.
Received: October 26, 2023
Accepted: December 23, 2023
References
J. Li and X. Zou, Modeling spatial spread of infectious diseases with a spatially continuous domain, Bulletin of Mathematical Biology 71(8) (2009), 20-48.
C. I. Siettos and L. Russo, Mathematical modeling of infectious disease dynamics, Virulence 4 (2013), 295-306.
S. M. Jenness, S. M. Goodreau and M. Morris, Epimodel: An R package for mathematical modeling of infectious disease over networks, Journal of Statistical Software 84 (2018), 1-56.
A. S. Shaikh, I. N. Shaikh and K. S. Nisar, A mathematical model of COVID-19 using fractional derivative: Outbreak in India with dynamics of transmission and control, Advances in Difference Equations 373 (2020), 1-19.
J. G. De Abajo, Simple mathematics on COVID-19 expansion, MedRxiv, 2020.
K. A. Gepreel, M. S. Mohamed, H. Alotaibi and A. M. S. Mahdy, Dynamical behaviors of nonlinear coronavirus (COVID-19) model with numerical studies, Computers, Materials and Continua 67(1) (2021), 675-686.
DOI:10.32604/cmc.2021.012200
K. Ghosh and A. K. Ghosh, Study of COVID-19 epidemiological evolution in India with a multi-wave SIR model, Nonlinear Dyn. 312(109) (2022), 47-55. https://doi.org/10.1007/s11071-022-07471-x
W. Alharbi, A. Shater, A. Ebaid, C. Cattani and M. Areshi, Communicable disease model in view of fractional calculus, AIMS Math. (8) (2023), 10033-10048.
A. Ebaid, Approximate analytical solution of a nonlinear boundary value problem and its application in fluid mechanics, Z. Naturforschung A 66 (2011), 423-426.
A. Ebaid, A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method, J. Comput. Appl. Math. 235 (2011), 1914-1924.
E. H. Ali, A. Ebaid and R. Rach, Advances in the Adomian decomposition method for solving two-point nonlinear boundary value problems with Neumann boundary conditions, Comput. Math. Appl. 63 (2012), 1056-1065.
A. Ebaid, C. Cattani, A. S. Al Juhani and E. R. El-Zahar, A novel exact solution for the fractional Ambartsumian equation, Adv. Differ. Equ. (2021), 2021:88. https://doi.org/10.1186/s13662-021-03235-w
A. Ebaid, M. D. Aljoufi and A.-M. Wazwaz, An advanced study on the solution of nanofluid flow problems via Adomian’s method, Appl. Math. Lett. 46 (2015), 117-122.
K. Abbaoui and Y. Cherruault, Convergence of Adomian’s method applied to nonlinear equations, Math. Comput. Model. 20 (1994), 69-73.
A. Alshaery and A. Ebaid, Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method, Acta Astronautica 140 (2017), 27-33.
H. O. Bakodah and A. Ebaid, Exact solution of Ambartsumian delay differential equation and comparison with Daftardar-Gejji and Jafari approximate method, Mathematics 6 (2018), 331.
A. Ebaid, A. Al-Enazi, B. Z. Albalawi and M. D. Aljoufi, Accurate approximate solution of Ambartsumian delay differential equation via decomposition method, Math. Comput. Appl. 24(1) (2019), 7.
A. H. S. Alenazy, A. Ebaid, E. A. Algehyne and H. K. Al-Jeaid, Advanced study on the delay differential equation Mathematics 10(22) (2022), 4302. https://doi.org/10.3390/math10224302
A. Ebaid, Remarks on the homotopy perturbation method for the peristaltic flow of Jeffrey fluid with nano-particles in an asymmetric channel, Computers and Mathematics with Applications 68(3) (2014), 77-85.
A. Ebaid, A. F. Aljohani and E. H. Aly, Homotopy perturbation method for peristaltic motion of gold-blood nanofluid with heat source, International Journal of Numerical Methods for Heat and Fluid Flow 30(6) (2020), 3121-3138. https://doi.org/10.1108/HFF-11-2018-0655
Ebrahem A. Algehyne, Essam R. El-Zahar, Fahad M. Alharbi and Abdelhalim Ebaid, Development of analytical solution for a generalized Ambartsumian equation, AIMS Mathematics 5(1) (2020), 249-258. doi: 10.3934/math.2020016
A. B. Albidah, N. E. Kanaan, A. Ebaid and H. K. Al-Jeaid, Exact and numerical analysis of the pantograph delay differential equation via the homotopy perturbation method, Mathematics 11 (2023), 944.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
