Before revision: In this paper, we conduct mathematical and numerical analyses  for COVID-19 . To predict the trend of COVID-19 , we propose a time-dependent SIR model that tracks  the transmission rate and the recovering rate at time t.
After revision: In this paper, we conduct mathematical and numerical analyses for COVID-19 . To predict the trend of COVID-19 ? (Q2) If COVID-19 can be contained, when will be the peak and the end of the epidemic? (Q3) How do the asymptomatic infections affect the spread of disease? (Q4) If COVID-19 cannot be contained, what is the ratio of the population that needs to be infected to achieve herd immunity? (Q5) How effective are the social distancing approaches? For (Q1) and (Q2), we propose a time-dependent SIR model that tracks the transmission rate and the recovering rate at time t.