Acquired Syphilis in Southern Brazil: Future Estimate of New Cases Using the Seasonal Autoregressive Integrated Moving Average (Sarima) Model

Acquired syphilis is a public health challenge in southern Brazil. In this context, prediction models can support planning for disease control. This study aimed to estimate acquired syphilis cases in southern Brazil using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model. Public data from the Notifiable Diseases Information System on monthly notifications of new acquired syphilis cases in Brazil from 2014 to 2023 were used. Sociodemographic variables included sex, age group, and race/skin color. The SARIMA model operates using autocorrelation and partial autocorrelation functions and logarithmic differencing. Stationarity was tested with the Augmented Dickey-Fuller test, trend with the Mann-Kendall test, autocorrelation with the Ljung-Box test, and best fit with the Akaike Information Criterion. SARIMA(p, d, q)(P, D, Q)s notation indicates the order of autoregressive terms, moving average terms, number of differences, and seasonal period, respectively. Model validation used mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE). The model was implemented in Python using StatsForecast, Statsmodels, and pyMannKendall libraries. A p-value ≤ 0.05 was considered statistically significant. The time series showed non-stationarity (Augmented Dickey-Fuller, p > 0.05), an upward trend (Mann-Kendall), autocorrelation (Ljung-Box, p 0.05). Forecasts for 2024 and 2025 indicate persistently high case numbers, with a peak in March 2024 (4,182 cases) and a monthly average of 3,470 cases by the end of 2025. Analyses by race/skin color showed increasing trends in all categories, with positive stationarity for Black, mixed-race, and Indigenous populations. Men and women had stationary series with an upward trend. Age groups up to 20 years and 60+ were stationary; the others were not. All age groups showed an increasing trend. No subcategory showed autocorrelation. The SARIMA model proved adequate to estimate acquired syphilis trends in southern Brazil for the next two years. The findings reinforce the importance of predictive models in epidemiological surveillance strategies.