COVID-19 pandemic has become a concern of every nation, and it is crucial to apply an estimation model with a favorably-high accuracy to provide an accurate perspective of the situation. In this study, three explicit mathematical prediction models were applied to forecast the COVID-19 outbreak in Iran and Turkey. These models include a recursive-based method, Boltzmann Function-based model and Beesham's prediction model. These models were exploited to analyze the confirmed and death cases of the first 106 and 87 days of the COVID-19 outbreak in Iran and Turkey, respectively. This application indicates that the three models fail to predict the first 10 to 20 days of data, depending on the prediction model. On the other hand, the results obtained for the rest of the data demonstrate that the three prediction models achieve high values for the determination coefficient, whereas they yielded to different average absolute relative errors. Based on the comparison, the recursive-based model performs the best, while it estimated the COVID-19 outbreak in Iran better than that of in Turkey. Impacts of applying or relaxing control measurements like curfew in Turkey and reopening the low-risk businesses in Iran were investigated through the recursive-based model. Finally, the results demonstrate the merit of the recursive-based model in analyzing various scenarios, which may provide suitable information for health politicians and public health decision-makers.