Mathematical Modeling and Forecasting of COVID-19 in Saudi Arabia under Fractal-Fractional Derivative in Caputo Sense with Power-Law
Open Access
- 15 September 2021
- Vol. 10 (3), 228
- https://doi.org/10.3390/axioms10030228
Abstract
This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order and fractal dimension . We give some detailed analysis on the existence and uniqueness of the solution to the proposed problem. Furthermore, some results regarding basic reproduction number and stability are given. For the proposed theoretical analysis, we use fixed point theory while for numerical analysis fractional Adams–Bashforth iterative techniques are utilized. Using our numerical scheme is verified by using some real values of the parameters to plot the approximate solution to the considered model. Graphical presentations corresponding to different values of fractional order and fractal dimensions are given. Moreover, we provide some information regarding the real data of Saudi Arabia from 1 March 2020 till 22 April 2021, then calculated the fatality rates by utilizing the SPSS, Eviews and Expert Modeler procedure. We also built forecasts of infection for the period 23 April 2021 to 30 May 2021, with 95% confidence.
Funding Information
- Al-Imam Muhammad Ibn Saud Islamic University (21-13-18-057)
This publication has 23 references indexed in Scilit:
- Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivativeAlexandria Engineering Journal, 2020
- Mathematical analysis of dengue fever outbreak by novel fractional operators with field dataPhysica A: Statistical Mechanics and its Applications, 2019
- A fractional model for the dynamics of competition between commercial and rural banks in IndonesiaChaos, Solitons, and Fractals, 2019
- A fractional model for the dynamics of TB virusChaos, Solitons, and Fractals, 2018
- Modelling and sensitivity analysis of river flow in the Upper Indus Basin, PakistanInternational Journal of Water, 2018
- New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic modelsThe European Physical Journal Plus, 2017
- New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer modelThermal Science, 2016
- Application of time-series analyses to the hydrological functioning of an Alpine karstic system: the case of Bange-L’Eau-MorteHydrology and Earth System Sciences, 2004
- Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmissionMathematical Biosciences, 2002
- On a measure of lack of fit in time series modelsBiometrika, 1978