Background COVID-19 poses a severe threat to global human health, especially the USA, Brazil, and India cases continue to increase dynamically, which has a far-reaching impact on people's health, social activities, and the local economic situation. Methods The study proposed the ARIMA, SARIMA and Prophet models to predict daily new cases and cumulative confirmed cases in the USA, Brazil and India over the next 30 days based on the COVID-19 new confirmed cases and cumulative confirmed cases data set(May 1, 2020, and November 30, 2021) published by the official WHO, Three models were implemented in the R 4.1.1 software with forecast and prophet package. The performance of different models was evaluated by using root mean square error (RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE). Results Through the fitting and prediction of daily new case data, we reveal that the Prophet model has more advantages in the prediction of the COVID-19 of the USA, which could compose data components and capture periodic characteristics when the data changes significantly, while SARIMA is more likely to appear over-fitting in the USA. And the SARIMA model captured a seven-day period hidden in daily COVID-19 new cases from 3 countries. While in the prediction of new cumulative cases, the ARIMA model has a better ability to fit and predict the data with a positive growth trend in different countries(Brazil and India). Conclusions This study can shed light on understanding the outbreak trends and give an insight into the epidemiological control of these regions. Further, the prediction of the Prophet model showed sufficient accuracy in the daily COVID-19 new cases of the USA. The ARIMA model is suitable for predicting Brazil and India, which can help take precautions and policy formulation for this epidemic in other countries.

At present, COVID-19 poses a serious threat to global human health, and the cumulative confirmed cases in America, Brazil and India continue to grow rapidly. Therefore, the prediction models of cumulative confirmed cases in America, Brazil and India from August 1, 2021 to December 31, 2021 were established. In this study, the prevalence data of COVID-19 from 1 August 2021 to 31 December 2021 were collected from the World Health Organization website. Several ARIMA models were formulated with different ARIMA parameters. ARIMA (7,2,0), ARIMA (3,2,1), and ARIMA (10,2,4) models with the lowest MAPE values (0.00132, 0.00048, and 0.00021) were selected as the best models for America, Brazil, and India, respectively. Initial combinations of model parameters were selected using the automated ARIMA model, and the optimized model parameters were then found based on Bayesian information criterion (BIC). The analytical tools autocorrelation function (ACF), and partial autocorrelation function (PACF) were used to evaluate the reliability of the model. The performance of different models in predicting confirmed cases from January 1, 2022 to January 5, 2022 was compared by using root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). This study shows that ARIMA models are suitable for predicting the prevalence of COVID-19 in the future. The results of the analysis can shed light on understanding the trends of the outbreak and give an idea of the epidemiological stage of these regions. Besides, the prediction of COVID-19 prevalence trends of America, Brazil, and India can help take precautions and policy formulation for this epidemic in other countries.