Numerical solutions and simulations of the fractional COVID-19 model via Pell-Lucas collocation algorithm

Abstract

The aim of this study is to present the evolution of COVID-19 pandemic in Turkey. For this, the SIR (Susceptible, Infected, Removed) model with the fractional order derivative is employed. By applying the collocation method via the Pell-Lucas polynomials (PLPs) to this model, the approximate solutions of model with fractional order derivative are obtained. Hence, the comments are made about the susceptible population, the infected population, and the recovered population. For the method, firstly, PLPs are expressed in matrix form for a selected number of N$$ N $$. With the help of this matrix relationship, the matrix forms of each term in the SIR model with the fractional order derivative are constituted. For implementation and visualization, we utilize MATLAB. Moreover, the outcomes for the Runge-Kutta method (RKM) are obtained using MATLAB, and these results are compared with the results obtained with the Pell-Lucas collocation method (PLCM). From all simulations, it is concluded that the presented method is effective and reliable.