Theoretical and numerical analysis of novel COVID-19 via fractional order mathematical model

Amjad Ali; Muhammad Yasin Khan; Muhammad Sinan; F M Allehiany; Emad E Mahmoud; Abdel-Haleem Abdel-Aty; Gohar Ali

doi:10.1016/j.rinp.2020.103676

Theoretical and numerical analysis of novel COVID-19 via fractional order mathematical model

Results Phys. 2021 Jan:20:103676. doi: 10.1016/j.rinp.2020.103676. Epub 2020 Dec 10.

Authors

Amjad Ali¹, Muhammad Yasin Khan², Muhammad Sinan³, F M Allehiany⁴, Emad E Mahmoud^{5

6}, Abdel-Haleem Abdel-Aty^{7

8}, Gohar Ali²

Affiliations

¹ Department of Mathematics, Govt P.G Jahanzeb College Swat, Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematics, Islamia College University, Peshawar, Khyber Pakhtunkhwa, Pakistan.
³ Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtunkhwa, Pakistan.
⁴ Department of Mathematical Sciences, College of Applied Sciences, Umm Al-Qura University, P.O. Box 715, Makkah 21955, Saudi Arabia.
⁵ Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
⁶ Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt.
⁷ Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia.
⁸ Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.

Abstract

In the work, author's presents a very significant and important issues related to the health of mankind's. Which is extremely important to realize the complex dynamic of inflected disease. With the help of Caputo fractional derivative, We capture the epidemiological system for the transmission of Novel Coronavirus-19 Infectious Disease (nCOVID-19). We constructed the model in four compartments susceptible, exposed, infected and recovered. We obtained the conditions for existence and Ulam's type stability for proposed system by using the tools of non-linear analysis. The author's thoroughly discussed the local and global asymptotical stabilities of underling model upon the disease free, endemic equilibrium and reproductive number. We used the techniques of Laplace Adomian decomposition method for the approximate solution of consider system. Furthermore, author's interpret the dynamics of proposed system graphically via Mathematica, from which we observed that disease can be either controlled to a large extent or eliminate, if transmission rate is reduced and increase the rate of treatment.

Keywords: 26A33; 34A08; 35B40; Approximate Solutions; Fixed point theory; Laplace-Adomian decomposition method; Mathematical modeling; Ulams type Stabilities; keyword: Fractional Derivatives.