Fractal-fractional mathematical modeling and forecasting of new cases and deaths of COVID-19 epidemic outbreaks in India

Mansour A Abdulwasaa; Mohammed S Abdo; Kamal Shah; Taher A Nofal; Satish K Panchal; Sunil V Kawale; Abdel-Haleem Abdel-Aty

doi:10.1016/j.rinp.2020.103702

Fractal-fractional mathematical modeling and forecasting of new cases and deaths of COVID-19 epidemic outbreaks in India

Results Phys. 2021 Jan:20:103702. doi: 10.1016/j.rinp.2020.103702. Epub 2020 Dec 15.

Authors

Mansour A Abdulwasaa¹, Mohammed S Abdo^{2

3}, Kamal Shah⁴, Taher A Nofal⁵, Satish K Panchal², Sunil V Kawale¹, Abdel-Haleem Abdel-Aty^{6

7}

Affiliations

¹ Department of Statistics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S), India.
² Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S), India.
³ Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen.
⁴ Department of Mathematics, University of Malakand, Chakdara Dir(Lower), Khyber Pakhtunkhawa, Pakistan.
⁵ Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
⁶ Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia.
⁷ Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.

Abstract

Fractional-order derivative-based modeling is very significant to describe real-world problems with forecasting and analyze the realistic situation of the proposed model. The aim of this work is to predict future trends in the behavior of the COVID-19 epidemic of confirmed cases and deaths in India for October 2020, using the expert modeler model and statistical analysis programs (SPSS version 23 & Eviews version 9). We also generalize a mathematical model based on a fractal fractional operator to investigate the existing outbreak of this disease. Our model describes the diverse transmission passages in the infection dynamics and affirms the role of the environmental reservoir in the transmission and outbreak of this disease. We give an itemized analysis of the proposed model including, the equilibrium points analysis, reproductive number $R_{0}$ , and the positiveness of the model solutions. Besides, the existence, uniqueness, and Ulam-Hyers stability results are investigated of the suggested model via some fixed point technique. The fractional Adams Bashforth method is applied to solve the fractal fractional model. Finally, a brief discussion of the graphical results using the numerical simulation (Matlab version 16) is shown.

Keywords: 26A33; 34A08; 35B40; COVID-2019; Fixed point technique; Forecasting; Fractal-fractional derivatives; Fractional Adams Bashforth method; SPSS program and Expert Modeler Method.