A Time-dependent SIR model for COVID-19

In this paper, we propose a mathematical model for analyzing and predicting the number of confirmed cases of COVID-19. Our model is a time-dependent susceptible-infected-recovered (SIR) model that tracks two time series: (i) the transmission rate at time $t$ and (ii) the recovering rate at time $t$. Our time-dependent SIR method is better than the traditional static SIR model as it can adapt to the change of contagious disease control policies such as city lockdowns. Moreover, it is also more robust than the direct estimation of the number of confirmed cases, as a sudden change of the definition of the number of confirmed cases might result in a spike of the number of new cases. Using the data set provided by the National Health Commission of the People's Republic of China (NHC) [2], we show that the one-day prediction errors for the numbers of confirmed cases are less than $3\%$ except the day when the definition of the number of confirmed cases is changed. Also, the turning point, defined as the day that the transmission rate is less than the recovering rate, is predicted to be Feb. 17, 2020. After that day, the basic reproduction number, known as the $R_0(t)$ value, is less than $1$ if the current contagious disease control policies are maintained in China. In that case, the total number of confirmed cases is predicted to be less than $80,000$ cases in China under our deterministic model.