EXISTENCE AND STABILITY ANALYSIS OF A FRACTIONAL-ORDER COVID-19 MODEL

Abstract

After the first confirmed case of coronavirus disease COVID-19 in Pakistan on February 26, 2020, the number of cases increases rapidly and as of April 20, 2020, 11:00 AM, the number of confirmed cases reached 271,887 out of which 5,787 died. Considering the situation, we develop a modified SEIR model of novel coronavirus (nCoV-19) keeping in view the transmission of pandemics in Pakistan. We generalize the proposed model to fractional-order derivatives in the Atangana-Baleanu sense. Moreover, we show the existence and uniqueness of solutions of the proposed fractional model using Schaefer’s and Banach’s fixed point theory, and utilizing the Sumudu transform and Picard’s successive approximation method, we explore the iterative solutions and their stability. In addition, using the least square curve fitting method together with the fminsearch function in the MATLAB optimization toolbox, we obtain the best values for some of the unknown biological parameters involved in the proposed model. Furthermore, we solved the fractional model numerically using the Atangana-Toufik numerical scheme and presented the different forms of graphical results that can be useful in minimizing the infection.