Numerical solution of fractional order SIR model of dengue fever disease via Laplace optimized decomposition method
Authors
B. Maayah
- Department of Mathematics, Faculty of Science, The University of Jordan, 11942, Amman, Jordan.
S. Bushnaq
- Department of Basic Sciences, Princess Sumaya University for Technology, 11941, Amman, , Jordan.
A. Moussaoui
- Department of Mathematics, Faculty of Science, The University of Jordan, 11942, Amman, Jordan.
Abstract
In this research article, we handle the susceptible infected-recovered (SIR) model of the dengue fever epidemic under Caputo Fabrizio fractional derivative. The dengue fever disease is a complicated disease because of the connection it creates between humans and mosquitoes. This encouraged scientists to understand the various factors that influence the recurrence of dengue fever. A new technique called the Laplace Optimized Decomposition (LODM) is used to solve this model numerically and compared with the 4\(^{\rm th}\) order Runge-Kutta Method (RKM). The solution in the proposed method is in the form of a convergent series with easily computable components. We present the solution via graphs and hence give some remarks about the nature of the solutions.
Share and Cite
ISRP Style
B. Maayah, S. Bushnaq, A. Moussaoui, Numerical solution of fractional order SIR model of dengue fever disease via Laplace optimized decomposition method, Journal of Mathematics and Computer Science, 32 (2024), no. 1, 86--93
AMA Style
Maayah B., Bushnaq S., Moussaoui A., Numerical solution of fractional order SIR model of dengue fever disease via Laplace optimized decomposition method. J Math Comput SCI-JM. (2024); 32(1):86--93
Chicago/Turabian Style
Maayah, B., Bushnaq, S., Moussaoui, A.. "Numerical solution of fractional order SIR model of dengue fever disease via Laplace optimized decomposition method." Journal of Mathematics and Computer Science, 32, no. 1 (2024): 86--93
Keywords
- Laplace optimized decomposition method (LODM)
- Caputo Fabrizio fractional derivative (CFFD)
- dengue fever epidemic model
MSC
References
-
[1]
G. Adomian, A review of the decomposition method in applied mathematics, A review of the decomposition method in applied mathematics, 135 (1988), 501–544
-
[2]
G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Comput. Math. Appl., 21 (1991), 101–127
-
[3]
S. Ahmad, S. Javeed, H. Ahmad, J. Khushi, S. K. Elagan, A. Khames, Analysis and numerical solution of novel fractional model for dengue, Results Phys., 28 (2021), 1–9
-
[4]
S. Alizadeh, D. Baleanu, S. Rezapour, Analyzing transient response of the parallel RCL circuit by using the Caputo- Fabrizio fractional derivative, Adv. Difference Equ., 2020 (2020), 1–19
-
[5]
D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional calculus: models and numerical methods, World Sci., (2012)
-
[6]
S. Bushnaq, T. Saed, D. F. M Torres, A. Zeb, Control of COVID-19 dynamics through a fractional-order model, Alex. Eng. J., 60 (2021), 3587–3592
-
[7]
O. Gonz´alez-Gaxiola, The Laplace-Adomian decomposition method applied to the Kundu-Eckhaus equation, Int. J. Math. Appl., 5 (2017), 1–12
-
[8]
M. Khalid, M. Sultana, F. S. Khan, Numerical solution of SIR model of dengue fever, Int. J. Comput. Appl., 118 (2015), 1–4
-
[9]
M. Khalid, M. Sultana, F. Sami, Numerical solution of SIR model of Dengue fever, Int. J. Comput. Appl., 118 (2015), 1–10
-
[10]
H. Khan, R. Shah, P. Kumam, D. Baleanu, M. Arif, Laplace decomposition for solving nonlinear system of fractional order partial differential equations, Adv. Difference Equ., 2020 (2020), 1–18
-
[11]
K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, Wiley, (1993)
-
[12]
A. Mohammed, A. Thabet, Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel, Adv. Difference Equ., 2017 (2017), 1–12
-
[13]
Z. Odibat, An Optimized decomposition method for nonlinear ordinary and partial differentail equations, Phys. A, 541 (2020), 13 pages
-
[14]
Z. Odibat, The optimized decomposition method for a reliable treatment of IVPs for second order differential equations, Phys. Scr., 96 (2021),
-
[15]
K. M. Owolabi, A. Atangana, Numerical methods for fractional differentiation, Springer, Singapore (2019)
-
[16]
N. R. Ramadhan, S. Side, S. Sidjara, Irwan, W. Sanusi, Numerical solution of SIRS model for transmission of dengue fever using Homptopy Perturbation Method in Makassar, AIP Conf. Prc., 2192 (2019), 1–8
-
[17]
S. Z. Rida, A. A. M. Arafa, Y. A Gaber, Solution of the fractional epidemic model by L-ADM, J. Fract. Calc. Appl., 7 (2016), 189–195
-
[18]
W. Sanusi, M. Pratama, M. Rifandi, S. Sidjara, Irwan, S. Side, Numerical Solution of SIRS model for Dengue Fever Transmission in Makassar City Runge Kutta Method, J. Phys.: Conf. Ser., 1752 (2019), 1–11
-
[19]
K. Shah, F. Jarad, T. Abdeljawad, On a nonlinear fractional order model of dengue fever disease under Caputo-Fabrizio derivative, Alex. Eng. J., 59 (2020), 2305–2313
-
[20]
R. Shah, H. Khan, M. Arif, P. Kumam, Application of Laplace-Adomian decomposition method for the analytical solution of third-order dispersive fractional partial differential equations, Entropy, 21 (2019), 17 pages
-
[21]
Q. Wang, Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method, Appl. Math. Comput., 182 (2006), 1048–1055
-
[22]
M. Zurigat, Solving nonlinear fractional differential equation using a multistep Laplace Adomian decomposition method, An. Univ. Craiova Ser. Mat. Inform., 39 (2012), 200–210