Time series prediction for the epidemic trends of monkeypox using the ARIMA, exponential smoothing, GM (1, 1) and LSTM deep learning methods

Monkeypox is a critical public health emergency with international implications. Few confirmed monkeypox cases had previously been reported outside endemic countries. However, since May 2022, the number of monkeypox infections has increased exponentially in non-endemic countries, especially in North America and Europe. The objective of this study was to develop optimal models for predicting daily cumulative confirmed monkeypox cases to help improve public health strategies. Autoregressive integrated moving average (ARIMA), exponential smoothing, long short-term memory (LSTM) and GM (1, 1) models were employed to fit the cumulative cases in the world, the USA, Spain, Germany, the UK and France. Performance was evaluated by minimum mean absolute percentage error (MAPE), among other metrics. The ARIMA (2, 2, 1) model performed best on the global monkeypox dataset, with a MAPE value of 0.040, while ARIMA (2, 2, 3) performed the best on the USA and French datasets, with MAPE values of 0.164 and 0.043, respectively. The exponential smoothing model showed superior performance on the Spanish, German and UK datasets, with MAPE values of 0.043, 0.015 and 0.021, respectively. In conclusion, an appropriate model should be selected according to the local epidemic characteristics, which is crucial for monitoring the monkeypox epidemic. Monkeypox epidemics remain severe, especially in North America and Europe, e.g. in the USA and Spain. The development of a comprehensive, evidence-based scientific programme at all levels is critical to controlling the spread of monkeypox infection.