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 %DIFDELCMD < \\%%% %DIF < 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.abstract 
In this paper, we propose two mathematical models for analyzing and predicting the number of confirmed cases of COVID-19. Our first model is a time-dependent susceptible-infected-recovered (SIR) model that tracks two time series , the transmission rate at time t , and 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 confirmed cases might result in a spike in the number of new cases. Using the data provided by the National Health Commission of the People's Republic of China [ 1 ], we show that the one-day prediction errors for the numbers of confirmed cases are almost less than 3 %DIFDELCMD < \\%%% %DIF < 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.abstract \%. 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 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 around 80,000 cases in China under our deterministic model. One problem for the first model is that there are asymptomatic infections for COVID-19. To model this, we propose our second SIR model that has two types of infected persons: detectable infected persons (type I) and undetectable infected cases (type II). To analyze whether there is an outbreak in such a model is characterized by the spectral radius of a 2 by 2 matrix that is closely related to the basic reproduction number. Our numerical results show that there are several countries, including South Korea, Italy, and Iran, that are above the percolation threshold curve, and they are on the verge of COVID-19 outbreaks on Mar. 2, 2020.
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\%. 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 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 around 80,000 cases in China under our deterministic model. One problem for the first model is that there are asymptomatic infections for COVID-19. To model this, we propose our second SIR model that has two types of infected persons: detectable infected persons (type I) and undetectable infected cases (type II). To analyze whether there is an outbreak in such a model is characterized by the spectral radius of a 2 by 2 matrix that is closely related to the basic reproduction number. Our numerical results show that there are several countries, including South Korea, Italy, and Iran, that are above the percolation threshold curve, and they are on the verge of COVID-19 outbreaks on Mar. 2, 2020.