Piecewise Fractional Analysis of Omicron Type Covid-19 Infection

Abstract

In this article, we investigate the new type of COVID-19 caused by the Omicron virus in the sense of piece-wise fractional derivative. The total interval is divided into two sub-intervals under fractional Caputo and Atangana Baleanu operators respectively. The whole model is divided into six compartments in which the agent of infection from Omicron is included. The proposed piecewise fractional model is tested for fixed points using the different theorems of fixed point theory. The approximate solution is carried out by the technique of the piecewise fractional Adams-Bashforth method. All the agents of the considered problem are tested for graphical representation. The first sub-interval is graphed for the Caputo derivative while the second interval dynamics are checked by Atangana Baleanu fractional operator. The numerical simulation results are established at different fractional orders along with the comparison of integer orders. This consideration will also show the cross-over behavior of the Omicron dynamics in human life and will be essential for its controlling and future prediction on various sub-intervals. The sensitivity of different parameters is also checked graphically.

Keywords: Piecewise Fractional Derivative, Fractional mathematical model Omicron; Qualitative analysis; Caputo derivative; Fractional Adams-Bashforth technique.