Numerical solutions of SIRD model of Covid-19 by utilizing Pell-Lucas collocation method - Yıldırım, Gamze; Yüzbaşı, Şuayip; Yüzbaşı, Şuayip (Tubitak Scientific & Technological Research Council Turkey, 2024)
This article presents an SIRD model based on the evolution of Coronavirus Disease 2019 (COVID-19) caused by SARS-CoV-2 from the coronavirus family. Firstly, we constitute Pell-Lucas collocation method (PLCM) for this model. According to method, the matrix forms of the Pell-Lucas polynomials (PLPs) are constituted. By utilizing this matrix forms, solution forms and all terms in this model are expressed in matrix form. Thus, PLCM transforms our model into a system of the matrix equations. By solving this system, the approximate solutions are obtained. In addition, the error analysis is also presented. In the examples of this study, we analyzed the T & uuml;rkiye's situation using initial datas and the parameters for T & uuml;rkiye. For this, we make applications for two different scenarios. In these two scenarios, the parameters, the initial conditions and the selected range are different. By considering the initial data and the parameters for other countries, this method can be applied to them, too. Application results are tabulated and visualized. Moreover, by comparing our results with Runge-Kutta method (RKM), the effectiveness of method is demonstrated. This study allows the identification of trends in the pandemic.
Numerical solutions of SIRD model of Covid-19 by utilizing Pell-Lucas collocation method
Keywords: Collocation Method; Covid-19; Mathematical Modeling; Nonlinear Differential Equations; Pell-Lucas Polynomials; Sird Model