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This paper analyzes single and two-wave COVID-19 outbreaks using two novel hybrid models, which combine machine learning and statistical methods with Richards growth models, to simulate and forecast the spread of the infection. For this purpose, historical cumulative numbers of confirmed cases for three countries, including Iran, Italy, and Mexico, are used. The analysis of the Richards models shows that its single-stage form can model the cumulative number of infections in countries with a single wave of outbreak (Italy and Mexico) accurately while its performance deteriorates for countries with two-wave outbreaks (Iran), which clarifies the requirement of multi-stage Richards models. The results of multi-stage Richards models reveal that the prevention of the second wave could reduce the outbreak size in Iran by approximately 400,000 cases, and the pandemic could be controlled almost 7 months earlier. Although the cumulative size of outbreak is estimated accurately using multi-stage Richards models, the results show that these models cannot forecast the daily number of cases, which are important for health systems’ planning. Therefore, two novel hybrid models, including autoregressive integrated moving average (ARIMA)-Richards and nonlinear autoregressive neural network (NAR)-Richards, are proposed. The accuracy of these models in forecasting the number of daily cases for 14 days ahead is calculated using the test data set shows that forecast error ranges from 8 to 25%. A comparison between these hybrid models also shows that the machine learning-based models have superior performance compared with statistical-based ones and on average are 20% more accurate.