A note on epidemiologic models: SIR modeling of the COVID-19 with variable coefficients

Abstract

The coronavirus disease 2019 (COVID-19) has been responsible for over three million reported cases worldwide. The construction of an appropriate mathematical (epidemiological) model for this disease is a challenging task. In this paper, we first consider susceptible - infectious - recovered (SIR) model with constant parameters and obtain an approximate solution for the SIR model with varying coefficient as it is one of the simplest models and many models are derived from this framework. The numerical experiments confirm that the proposed formulation demonstrates similar characteristic behaviour with the well-known approximations.