Prediction of new cases of acquired syphilis in Brazil using the Seasonal Autoregressive Integrated Moving Average (SARIMA) and Long Short-Term Memory (LSTM) models

Abstract

Objective: to estimate new cases of acquired syphilis in Brazil using the Autoregressive Integrated Moving Average (SARIMA) model, the Long-Short-Term Memory (LSTM) model, and the arithmetic mean between them. Methods: data from the Notifiable Diseases Information System regarding monthly notifications between 2014 and 2023 were analyzed. Validation used the Mean Absolute Percentage Error (MAPE), the Root Mean Square Error (RMSE), and the Mean Absolute Error (MAE). Results: The series showed an increasing trend and annual seasonality. It was non-stationary (ADF p = 0.659) and exhibited autocorrelation (Ljung-Box p < 0.001). The SARIMA (0,1,2)(0,0,1)[12] and LSTM models were compared. Both models presented random residuals (Ljung-Box: SARIMA p = 0.068; LSTM p = 0.321). The metrics were close, with a slight advantage for SARIMA (RMSE 2.232 vs 2.422; MAE 1.891 vs 1.922; MAPE 10%). The arithmetic mean obtained better results in all error indices and independence from noise. SARIMA predictions stabilize at 19,800 cases from March 2025 onwards, while LSTM predictions decline to 18,960 in the same period. An increasing trend was observed in all population segments, and autocorrelation of the data was only present in the regional segment, indicating the need to consider the whole to understand the parts. Conclusions: both models were adequate for estimating cases of acquired syphilis, with no significant difference in accuracy, and with the arithmetic mean further increased the reliability of the predictions.