We propose a deterministic SAIVRD model and a stochastic SARV model of the epidemic COVID-19 involving asymptomatic infections and vaccinations to conduct data forecasts using time-dependent parameters. The forecast by our deterministic model conducts 10-day predictions to see whether the epidemic will ease or become more severe in the short term. The forecast by our stochastic model predicts the probability distributions of the final size and the maximum size to see how large the epidemic will be in the long run. The first forecast using the data set from the USA gives the relative errors within 3% in 5 days and 7% in 10 days for the prediction of isolated infectious cases and smaller ones for the predictions of recoveries and deaths. The distributions in the second forecast using the time-varying parameters from the first forecast are also bimodal in our model with time-independent parameters in our simulations of smaller populations. For the model with time-dependent model, what are different are that there is another peak in the final size distribution, that the the probability of minor outbreak is higher and that the maximum size distribution is oscillating with time-dependent parameters. The final size distributions are similar between different populations and so are the maximum size distributions, which means that we can expect that with the same parameters and in a large population, the ratio of the final size and the maximum size are distributed similarly (only different by the value of the second peak). The result shows that under recent transmissibility of this disease in the USA, when an initial infection is introduced into all-susceptible (large) population, major outbreak occurs with around 95% of the population and with high probability the epidemic is maximized to around 30% of the population.