Future Estimation of New Cases of Congenital Syphilis in Southern Brazil Using the Seasonal Autoregressive Integrated Moving Average (Sarima) Model

Syphilis is a sexually transmitted infection that can also be vertically transmitted. It is a cause of fetal mortality and therefore requires strong epidemiological surveillance. The objective of this study is to estimate congenital syphilis cases in southern Brazil up to June 2026 using the Seasonal Autoregressive Integrated Moving Average (SARIMA) model. The SARIMA model is adjusted by autocorrelation functions, partial autocorrelation, and logarithmic differentiation. It is expressed as SARIMA(p, d, q)(P, D, Q)s, where P and p represent the autoregressive order; Q and q, the moving average order; D and d, the number of differences; and s, the seasonal period. Stationarity was tested using the augmented Dickey-Fuller test, trend by the Mann-Kendall test, autocorrelation by the Ljung-Box test, and the best fit by the Akaike Information Criterion. Validation considered the mean absolute percentage error (MAPE), root mean square error (RMSE), and mean absolute error (MAE). Monthly congenital syphilis data from January 2014 to June 2024 were analyzed from the National Notifiable Diseases Information System (SINAN), including maternal race, sex, and age group. Modeling was performed in Python using the StatsForecast, Statsmodels, and pyMannKendall libraries. p-values ≤ 0.05 were considered significant. The series was stationary (p = 0.01), with an increasing trend, presence of autocorrelation (p = 3.3e-57), and seasonality. The best-fitting model was SARIMA(0,1,1)(2,0,0)12, showing good predictive performance (MAPE = 0.09; RMSE = 33.80; MAE = 25.50) and autocorrelation in residuals (p = 0.02). Projections indicated between 225 and 245 monthly cases from July 2024 to June 2026, with a peak in January 2025. No autocorrelation was observed by race, gender, or maternal age group, except among mothers under 20 years old. Stationarity was observed only in the Black race group, and an increasing trend was noted among Black and Yellow race groups. There was no trend or stationarity by gender. No maternal age group was stationary, and all showed an upward trend. The SARIMA model showed good accuracy in predicting congenital syphilis cases in southern Brazil for the next two years, even with non-independent residuals. Continuous application of this model is recommended as an epidemiological surveillance tool.