A fractional order SITR mathematical model for forecasting of transmission of COVID-19 of India with lockdown effect

S S Askar; Dipankar Ghosh; P K Santra; Abdelalim A Elsadany; G S Mahapatra

doi:10.1016/j.rinp.2021.104067

A fractional order SITR mathematical model for forecasting of transmission of COVID-19 of India with lockdown effect

Results Phys. 2021 May:24:104067. doi: 10.1016/j.rinp.2021.104067. Epub 2021 Mar 23.

Authors

S S Askar^{1

2}, Dipankar Ghosh³, P K Santra⁴, Abdelalim A Elsadany⁵, G S Mahapatra³

Affiliations

¹ Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia.
² Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
³ Department of Mathematics, National Institute of Technology Puducherry, Karaikal 609609, India.
⁴ Abada Nsup School, Howrah, West Bengal, India.
⁵ Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt.

Abstract

In this paper, we consider a mathematical model to explain, understanding, and to forecast the outbreaks of COVID-19 in India. The model has four components leading to a system of fractional order differential equations incorporating the refuge concept to study the lockdown effect in controlling COVID-19 spread in India. We investigate the model using the concept of Caputo fractional-order derivative. The goal of this model is to estimate the number of total infected, active cases, deaths, as well as recoveries from COVID-19 to control or minimize the above issues in India. The existence, uniqueness, non-negativity, and boundedness of the solutions are established. In addition, the local and global asymptotic stability of the equilibrium points of the fractional-order system and the basic reproduction number are studied for understanding and prediction of the transmission of COVID-19 in India. The next step is to carry out sensitivity analysis to find out which parameter is the most dominant to affect the disease's endemicity. The results reveal that the parameters $η, μ$ and $ρ$ are the most dominant sensitivity indices towards the basic reproductive number. A numerical illustration is presented via computer simulations using MATLAB to show a realistic point of view.

Keywords: COVID-19; Fractional differential equation; Lockdown; Refuge; Reproduction number; SITR compartmental model; Stability.