Dynamics of Fractional Order SIR Model with a Case Study of COVID-19 in Turkey

Zubair Ahmad, Muhammad Arif, Ilyas Khan

Abstract


The outbreak and propagation of novel coronavirus disease 2019 (COVID-19) have posed a considerable challenge to modern society. The susceptible-infected-recovered/removed (SIR) model and its variants are widely used to predict the progress of COVID 19 worldwide, despite their rather simplistic nature. Nevertheless, precise results of the SIR model present a significant challenge, particularly with limited and possibly noisy data in the initial phase of the pandemic. The present study aims to describe the dynamics of COVID-19 inTurkey. To investigate the spread of coronavirus in Turkey, we develop an SIR time-fractional model with a newly developed fractional operator of Atangana-Baleanu. We consider the available infection cases from 30th October 2020 till 8th November 2020, and accordingly, various parameters are fitted or estimated. We have calculated the basic reproduction number . Furthermore, stability analysis of the model at disease free equilibrium DFE and endemic equilibriums EE is performed to observe the dynamics and transmission of the model. Finally, the AB fractional model is solved numerically. To show the effect of the various embedded parameters like fractional parameter , contact rate ?, and ?on the model, various graphs are plotted. We have predicted the spread of the disease for the next 800 days.


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DOI: https://doi.org/10.33959/cuijca.v4i01.43

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