Modeling the Evolution of SARS-CoV-2 Using a Fractional-Order SIR Approach

Abstract

To show the potential of non-commensurable fractional-order dynamical systems in modeling epidemiological phenomena, we will adjust the parameters of a fractional generalization of the SIR model to describe the population distributions generated by SARS-CoV-2 in France and Colombia. Despite the completely different contexts of both countries, we will see how the system presented here manages to adequately model them thanks to the flexibility provided by the fractional-order differential equations. The data for Colombia were obtained from the records published by the Colombian Ministry of Information Technology and Communications from March 24 to July 10, 2020. Those for France were taken from the information published by the Ministry of Solidarity and Health from May 1 to September 6, 2020. As for the methodology implemented in this study, we conducted an exploratory analysis focused on solving the fractional SIR model by means of the fractional transformation method. In addition, the model parameters were adjusted using a sophisticated optimization method known as the Bound Optimization BY Quadratic Approximation (BOBYQA) algorithm. According to the results, the maximum error percentage for the evolution of the susceptible, infected, and recovered populations in France was 0.05%, 19%, and 6%, respectively, while that for the evolution of the susceptible, infected, and recovered populations in Colombia was 0.003%, 19%, and 38%, respectively. This was considered for data in which the disease began to spread and human intervention did not imply a substantial change in the community.