Fractional Modelling for COVID-19 in the World and Iraq
DOI:
https://doi.org/10.30526/37.2.3359Keywords:
Caputo Fractional Derivative; Riemann-Liouville Fractional Derivative; Fractional COVID-19 model; Numerical simulations; fractional linear multi-step method.Abstract
This article talks about a model of fractional differential equations to describe how COVID-19 is spread in the world in general and Iraq in particular. The model contains five fractional differential equations. Moreover, we have proven the existence and uniqueness of the solution of the model, found the equilibrium points of the model and checked its stability. Then we solved it using a fractional linear multi-step method. When we compare the results with the data documented by the World Health Organisation (WHO), we find that the total number of active cases in the world are equal to 584498294 on 3/8/2022, and it is similar to what was done with the system. The number of those who have recovered and died from the disease has also been calculated. For Iraq, the total number of active cases is 2448484 and the total number of active cases calculated by the model is 2628000. In comparison, the calculated number is slightly higher than what is given in the data. This is quite normal because not all infected patients go to the health centres and it is difficult to record them as active cases.
References
Tuan, N. H.; Mohammadi, H. ; Rezapour, S. A mathematical model for COVID-19 transmission by using the Caputo fractional derivative. Chaos, Solitons & Fractals, 2020, 140, 110107. https://doi.org/10.1016/j.chaos.2020.110107
Al-Saedi, H. M., ; Hameed, H. H. Mathematical modeling for COVID-19 pandemic in Iraq. J Interdiscip Math. 2021, 24(5), 1407–1427. https://doi.org/10.1080/09720502.2021.1923943
Ndaïrou, F.; Area, I.; Nieto, J. J.; Silva, C. J. ; Torres, D. F Fractional model of COVID-19 applied to Galicia, Spain and Portugal. Chaos, Solitons & Fractals, 2021, 144, 110652. https://doi.org/10.1016/j.chaos.2021.110652
Kareem, A. M.; Al-Azzawi, S. N. Comparison Between Deterministic and Stochastic Model for Interaction (COVID-19) With Host Cells in Humans. Baghdad Science Journal, 2022, 19(5), 1140-1140. https://doi.org/10.21123/bsj.2022.6111
Martcheva, M..An Introduction to Mathematical Epidemiology, New York: Springer. 2015, 61, 9-31. https://doi.org/10.1007/978-1-4899-7612-3
Yunus, A. A. B. M.; Yunus, A. A. B. M.; Ibrahim, M. S. B., ; Ismail, S. B. Future of Mathematical Modelling: A Review of COVID-19 Infected Cases Using S-I-R Model. Baghdad Science Journal. 2021, 18(1), 824–9. http://dx.doi.org/10.21123/bsj.2021.18.1(Suppl.).0824
Krishna, M. V. Mathematical modelling on diffusion and control of COVID–19. Infectious Disease Modelling. 2020, 5, 588–597 https://doi.org/10.1016/j.idm.2020.08.009
Ndaïrou, F.; Area, I.; Nieto, J. J.; Torres, D. F. Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan. Chaos, Solitons & Fractals, 2020, 135, 109846. https://doi.org/10.1016/j.chaos.2020.109846
Shah, N. H.; Mittal, M. (Eds.). Mathematical Analysis for Transmission of COVID-19.Springer Singapore, 2021.
Higazy, M.; Allehiany, F. M.; Mahmoud, E. E. Numerical study of fractional order COVID-19 pandemic transmission model in context of ABO blood group. Results in Physics, 2021, 22, 103852. https://doi.org/10.1016/j.rinp.2021.103852
Rezapour, S.; Mohammadi, H. ; Samei, M. E. SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order. Advances in difference equations, 2020, 1-19.https://doi.org/10.1186/s13662-020-02952-y
Abdulla, Z. K.; Al-Azzawi, S. N.. Solving the COVID-19 Fractional Model by Using Sumudu Transform and ADM. In AIP Conference Proceedings, 2023, 2839(1). AIP Publishing. https://doi.org/10.1063/5.0167781
Kai, D. The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type. In Lecture Notes in Mathematics. Springer. 2010.
http://dx.doi.org/10.1007/978-3-642-14574-2
Ati, R. R.; Al-Azzawi, S. N. Fractional Order Modification of Tuckwell and Wan Medical Model. In Journal of Physics: Conference Series 2021, 1818(1), 012028. IOP Publishing. http://dx.doi.org/10.1088/1742-6596/1818/1/012028
Mirevski, S. P.; Boyadjiev, L.; Scherer, R. On the Riemann–Liouville fractional calculus, g-Jacobi functions and F-Gauss functions. Applied Mathematics and Computation, 2007, 187(1), 315-325. https://dx.doi.org/10.1016/j.amc.2007.01.035
Diethelm, K.; Ford, N. J. Analysis of fractional differential equations. Journal of Mathematical Analysis and Applications, 2002, 265(2), 229-248.
https://doi.org/10.1006/jmaa.2000.7194
Tarasov, V. E. Fractional dynamics: applications of fractional calculus to dynamics of particles, fields and media. Springer Science & Business Media. 2011.
Zhang, W. B. Differential equations, bifurcations, and chaos in economics 2005 , 68. World Scientific.
Arrowsmith, D.; Place, C. M. Dynamical systems: differential equations, maps, and chaotic behavior. 1992,5. CRC Press. https://doi.org/10.1201/978131514154
Garrappa, R. Numerical solution of fractional differential equations: A survey and a software tutorial. Mathematics, 2018, 6(2), 16. https://doi.org/10.3390/math6020016
Owolabi, K. M. Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems. Chaos, Solitons & Fractals, 2016, 93, 89-98. https://doi.org/10.1016/j.chaos.2016.10.005.
Klages, R.. Introduction to dynamical systems. Lecture Notes for MAS424/MTHM021. Queen Mary University of London, 2008, 24, 26.
Malley Jr, R. E. The Theory of Differential Equations: Classical and Qualitative.: Classical and Qualitative. SIAM Review, 2005, 47(1), 185.
Derrick, W. R.; Grossman, S. I. Elementary differential equations with applications. 1976. https://lccn.loc.gov/80022057
Ahmad, S.; Ambrosetti, A. A textbook on ordinary differential equations. 2015, 88. Springer. https://doi.org/10.1007/978-3-319-16408-3
Hirsch, M. W.; Smale, S.; Devaney, R. L. Differential equations, dynamical systems, and an introduction to chaos. Academic press. 2012.
Dukkipati, R. V. MATLAB: an introduction with applications. New Age International. 2008.
Lynch, S. Dynamical systems with applications using MATLAB. Boston: Birkhäuser. 2004 .https://doi.org/10.1007/978-3-319-06820-6.
Burden, R. L. ; Faires, J. D. Numerical analysis (nineth edition). Thomson Brooks/Cole, 2010.
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