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

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.