Forecasting continued increase in primary and secondary syphilis in the United States, 2024–2033: a state-level multi-model ensemble study

Qiancheng Ma, Tianzhen Zhang, DTS Lin, Wenyuan Zou, Liuying Lin

Introduction Primary and secondary (P&S) syphilis burden in the United States has increased substantially in recent years, underscoring the need for forecasting approaches that can inform medium-term public health planning. Methods We assembled a state-level panel dataset covering 2003–2023 and evaluated five candidate forecasting models: autoregressive model of order 1 [AR(1)], a state-specific linear trend baseline, Bayesian negative binomial regression, neural network, and Extreme Gradient Boosting (XGBoost). Models were trained using historical state-level surveillance and covariate data and assessed on external holdout data. For the non-Bayesian models, prediction intervals were calibrated using a residual-based calibration approach, whereas Bayesian uncertainty was obtained from the posterior predictive distribution. A final top-3 global ensemble was constructed from the best-performing models. Results The final ensemble achieved a holdout weighted absolute percentage error (WAPE) of 20.8%. Under the continuation of the main historical patterns represented in the data, the national burden was projected to increase to approximately 131,736 cases in 2033. Projected cumulative burden was highest in California, Florida, New York, Texas, and Georgia, whereas the fastest relative growth was projected in Iowa, North Dakota, Wisconsin, South Dakota, and Nevada. Diagnostic analyses found no evidence of residual spatial autocorrelation in the final ensemble. Discussion This forecasting framework provides a practical approach for projecting state-level syphilis burden in the United States. It may support public health planning by distinguishing states with persistently high projected burden from those with comparatively rapid projected growth.