Analysis of COVID-19 spread in South Korea using the SIR model with time-dependent parameters and deep learning

Mathematical modeling is a process aimed at finding a mathematical description of a system and translating it into a relational expression. When a system is continuously changing over time (e.g., infectious diseases) differential equations, which may include parameters, are used for modeling the system. The process of finding those parameters that best fit the given data from the system is called an inverse problem. This study aims at analyzing the novel coronavirus infection (COVID-19) spread in South Korea using the susceptible-infected-recovered (SIR) model. We collect the data from Korea Centers for Disease Control & Prevention (KCDC). We assume that each parameter in the SIR model is a function of time so that we can compute important parameters, such as the basic reproduction number (R0), more delicately. Using neural networks, we propose a method to find the best time-varying parameters and the solution for the model simultaneously. Moreover, using time-dependent parameters, we find that traditional numerical algorithms, such as the Runge-Kutta methods, can successfully approximate the SIR model while fitting the COVID-19 data, thus modeling the propagation patterns of COVID-19 more precisely.