Numerical analysis of COVID-19 model with constant fractional order and variable fractal dimension

Badr Saad T Alkahtani; Sonal Jain

doi:10.1016/j.rinp.2020.103673

Numerical analysis of COVID-19 model with constant fractional order and variable fractal dimension

Results Phys. 2021 Jan:20:103673. doi: 10.1016/j.rinp.2020.103673. Epub 2020 Dec 10.

Authors

Badr Saad T Alkahtani¹, Sonal Jain²

Affiliations

¹ Department of Mathematics, College of Science, King Saud University, P.O. Box 1142, Riyadh 11989, Saudi Arabia.
² Department of Humanity and Sciences, Rizvi College of Engineering, Bandra West, Mumbai, Maharashtra 400050, India.

Abstract

This work has considered a mathematical model describing the spread of COVID-19 in a given population. The model comprised 5 systems of equations that take into account different classes describing the impact of COVID-19 in a given population. The time differential operator was replaced with three different types of nonlocal operators. These operators are defined as the convolution of variable order fractal differential operators with different kernels including power law, exponential decay law, and Mittag-Leffler functions. We presented the well-poseness of the models for different differential operators that were presented in detail. A novel numerical scheme was used to solve numerically the system and numerical simulations were provided.

Keywords: Keywords: COVID-19 model; Non-local operators; Novel numerical scheme; Well-poseness.