Evaluating syphilis transmission among MSM population: a mathematical model for reinfection, two-stage treatment, and treatment failure.

This study develops and analyzes a data-driven compartmental model for the transmission dynamics of syphilis among men who have sex with men (MSM) in the United States, incorporating reinfection, two-stage treatment, treatment failure and behavioral adaptation. The model comprises five epidemiological compartments with parameters that capture temporary immunity, adaptive behavior, and heterogeneous treatment outcomes. Analytical results include the derivation of the basic reproduction number ( R 0 ), stability analysis of equilibria, and conditions for backward bifurcation, revealing potential disease persistence even when R 0 < 1 . Using U.S. surveillance data from 2011 to 2023, joinpoint regression identified three major inflection periods 2017, 2019, and 2021 corresponding to shifts in epidemic trajectories. Model calibration demonstrated strong agreement with reported data, yielding MAPE = 14.41% and RMSE = 9376.66, thereby validating the model's predictive accuracy. Simulation and sensitivity analyses underscore the influence of reinfection, behavioral adaptation, and treatment efficacy on disease persistence. Decision-analytic evaluation indicates that a combined approach of enhanced screening, timely treatment, and doxycycline post-exposure prophylaxis can substantially reduce the syphilis burden. The proposed framework provides a robust, quantitative decision-support tool for optimizing intervention strategies among high-risk MSM populations.