A susceptible-infected-susceptible (SIS) model with a nonlinear infection rate, a forecast model based on autoregressive integrated moving average (ARIMA), and a forecast model based on long short-term memory (LSTM) artificial neural networks were developed using the COVID-19 epidemic data from four countries (China, Italy, the United Kingdom, Germany, France, and Poland) to simulate and forecast the epidemic trends in these countries. The models were compared in terms of forecast errors, and the LSTM model was found to forecast virus transmission very well.