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In this study, an individual-based epidemic model, considering latent-infectious-recovery periods, is presented. The analytic solution of the model in the form of recursive formulae with a time-dependent transmission coefficient is derived and implanted in Excel. The simulated epidemic curves from the model fit very well with the daily reported cases of COVID-19 in Wuhan, China and New York City (NYC), USA. These simulations show that the transmission rate of NYC’s COVID-19 is nearly 30% greater than the transmission rate of Wuhan’s COVID-19, and that the actual number of cumulative infected people in NYC is around 9 times the reported number of cumulative COVID-19 cases in NYC. Results from this study also provide important information about latent period, infectious period and lockdown efficiency.