Multi-step Adomian decomposition method for solving a delayed Chikungunya virus system

Volume 37, Issue 4, pp 361--372 https://dx.doi.org/10.22436/jmcs.037.04.01

Publication Date: October 26, 2024 Submission Date: May 05, 2024 Revision Date: July 01, 2024 Accteptance Date: September 06, 2024

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Authors

M. Chamekh - Mathematics Department, ‎University‎ ‎of Jeddah, ‎Jeddah, ‎Kingdom of Saudi Arabia (KSA). - University of Tunis El Manar, ‎National Engineering‎ ‎School at Tunis, ‎LAMSIN‎, ‎1002, Tunis, ‎Tunisia. M. A. Latrach - University of Tunis El Manar, ‎National Engineering‎ ‎School at Tunis, ‎LAMSIN‎, ‎1002‎, Tunis, ‎Tunisia. Y. Abed - Mathematics Department, ‎University‎ ‎of Jeddah, ‎Jeddah, ‎Kingdom of Saudi Arabia (KSA).

Abstract

‎This paper is an extension of work [M‎. ‎Chamekh‎, ‎M‎. ‎A‎. ‎Latrach‎, ‎F‎. ‎Jday‎, ‎J‎. ‎Umm Al-Qura Univ‎. ‎Appll‎. ‎Sci.‎, \(\bf 9\) (2023)‎, ‎123--131] in which we proposed a multi-step semi-analytical solution for a chikungunya virus system without delay‎. ‎Accordingly‎, ‎this work targets the same problem but with delay‎. ‎We first used the Lyapunov function method to present the theoretical stability analysis of the Chikungunya virus model with latency and with delay‎. ‎Afterwards‎, ‎we discussed the use of the Adomian decomposition method with a technique of multi-step to obtain a solution to a delayed Chikungunya problem in particular‎, ‎and we aimed in general at some problems of dynamical systems with delay‎. ‎To validate the accuracy and efficiency of this method‎, ‎the numerical results were discussed by comparing them to the Runge-Kutta method‎.

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Keywords

• Multi-step method‎
• Adomian decomposition method
• Chikungunya virus
• delay differential equations

MSC

•  92B05
•  37N30

References

• [1] O. Allix, J.-F. Deü, Delayed-Damage Modelling for Fracture Prediction of Laminated Composites under Dynamic Loading, Eng. Trans., 45 (1997), 29–46
  • View Article
  • Google Scholar


• [2] M. Al-Zurigat, Solving nonlinear fractional differential equation using a multi-step Laplace Adomian decomposition method, An. Univ. Craiova Ser. Mat. Inform., 39 (2012), 200–210
  • View Article
  • Google Scholar
  • MATH


• [3] E. Bayraktar, M. Egami, The effects of implementation delay on decision-making under uncertainty, Stochastic Process. Appl., 117 (2007), 333–358
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] L. Blanco-Cocom, A. G. Estrella, E. Avila-Vales, Solving delay differential systems with history functions by the Adomian decomposition method, Appl. Math. Comput., 218 (2012), 5994–6011
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] M. Chamekh, M. A. Latrach, F. Jday, Multi-step semi-analytical solutions for a chikungunya virus system, J. Umm Al-Qura Univ. Appll. Sci., 9 (2023), 123–131
  • View Article
  • Google Scholar


• [6] M. Chamekh, T. M. Elzaki, N. Brik, Semi-analytical solution for some proportional delay differential equations, SN Appl. Sci., 1 (2019), 6 pages
  • View Article
  • Google Scholar


• [7] N. Do˘gan, Solution of the system of ordinary differential equations by combined Laplace transform-Adomian decomposition method, Math. Comput. Appl., 17 (2012), 203–211
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] A. M. Elaiw, T. O. Alade, S. M. Alsulami, Analysis of latent CHIKV dynamics models with general incidence rate and time delays, J. Biol. Dyn., 12 (2018), 700–730
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] M. El Hajji, Periodic solutions for chikungunya virus dynamics in a seasonal environment with a general incidence rate, AIMS Math., 8 (2023), 24888–24913
  • View Article
  • Google Scholar


• [10] M. El Hajji, R. M. Alnjrani, Periodic behaviour of HIV dynamics with three infection routes, Mathematics, 12 (2024), 23 pages
  • View Article
  • Google Scholar


• [11] M. El Hajji, M. F. S. Aloufi, M. H. Alharbi, Influence of seasonality on Zika virus transmission, AIMS Math., 9 (2024), 19361–19384
  • View Article
  • MathSciNet
  • Google Scholar


• [12] M. El Hajji, A. Zaghdani, S. Sayari, Mathematical analysis and optimal control for Chikungunya virus with two routes of infection with nonlinear incidence rate, Int. J. Biomath., 15 (2022), 26 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [13] D. J. Evans, K. R. Raslan, The Adomian decomposition method for solving delay differential equation, Int. J. Comput. Math., 82 (2005), 49–54
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [14] S. E. Fadugba, V. J. Shaalini, M. O. Oluwayemi, M. C. Kekana, Applicability and analysis of trigonometric–exponential single–step method for the numerical solution of HIV-1 model, Commun. Math. Biol. Neurosci., 2023 (2023), 15 pages
  • View Article
  • Google Scholar


• [15] G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo, M. Colaneri, Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy, Nat. Med., 26 (2020), 855–860
  • View Article
  • Google Scholar


• [16] J. He, Variational iteration method for delay differential equations, Commun. Nonlinear Sci. Numer. Simul., 2 (1997), 235–236
  • View Article
  • Google Scholar
  • MATH


• [17] D. J. Higham, Robust defect control with Runge-Kutta schemes, SIAM J. Numer. Anal., 26 (1989), 1175–1183
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] T. Müller, M. Lauk, M. Reinhard, A. Hetzel, C. H. Lücking, J. Timmer, Estimation of Delay Times in Biological Systems, Ann. Biomed. Eng., 31 (2003), 1423–1439
  • View Article
  • Google Scholar


• [19] F. Karakoç, H. Bereketo˘ glu, Solution of delay differential equation by using differential transform, Int. J. Comput. Math., 86 (2009), 914–923
  • View Article
  • MathSciNet
  • Google Scholar


• [20] Y. Kuang, Delay differential equations with applications in population dynamics, Academic Press, Boston (1993)
  • View Article
  • Google Scholar


• [21] M. Rehim, Z. Zhang, A. Muhammadhaji, Mathematical analysis of a nutrient-plankton system with delay, SpringerPlus, 5 (2016), 22 pages
  • View Article
  • Google Scholar


• [22] M. R. Roussel, The Use of Delay Differential Equations in Chemical Kinetics, J. Phys. Chem., 100 (1996), 8323–8330
  • View Article
  • Google Scholar


• [23] J. V. Shaalini, A. E. K. Pushpam, An application of exponential–polynomial single–step method for solving viral model with delayed immune response, Adv. Math.: Sci. J., 8 (2019), 154–161
  • View Article
  • Google Scholar
  • MATH


• [24] F. Shakeri, M. Dehghan, Solution of delay differential equations via a homotopy perturbation method, Math. Comput. Modelling, 48 (2008), 486–498
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] L. F. Shampine, Interpolation for Runge-Kutta methods, SIAM J. Numer. Anal., 22 (1985), 1014–1027
  • View Article
  • MathSciNet
  • Google Scholar


• [26] H. Smith, An introduction to delay differential equations with applications to the life sciences, Springer, New York (2011)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [27] A.-M. Wazwaz, Necessary conditions for the appearance of noise terms in decomposition solution series, Appl. Math. Comput., 81 (1997), 265–274
  • View Article
  • Google Scholar
  • MATH


• [28] A.-M. Wazwaz, The existence of noise terms for systems of inhomogeneous differential and integral equations, Appl. Math. Comput., 146 (2003), 81–92
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [29] J. K. Zhou, Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuuhahn, China (1986)
  • View Article
  • Google Scholar