Syphilis is a highly contagious bacterial disease with different stages which results in substantial morbidity and mortality worldwide. In particular, it has been resurging among all age groups in both developed and developing countries in the last a few years after the COVID-19 pandemic. Since sexual contact is the main transmission mode, age structure of the host is crucial for the spread of syphilis. In this talk, we introduce an age-structured epidemic model with four infection stages (primary, secondary, latent, and tertiary) to study the transmission dynamics of syphilis. First we establish the well-posedness of the initial–boundary value problem and derive an explicit expression of the basic reproduction number. Then we study global stability of the disease-free steady state and the uniqueness and local stability of the endemic steady state. Next we consider the optimal control of the age-structured model and calibrate the reported data in China by using a demographic model utilizing the Markov Chain Monte Carlo method. Finally, we apply the relevant simulation results to numerically simulate the age-structured model. Our results indicate that (i) for the syphilis demographic model the basic reproduction number R_0=2.4876 with CI (95%) (1.6823, 3.1434) in China; (ii) tertiary stage infection is more severe in the elderly population; (iii) reducing the number of secondary and latent stage syphilis individuals can effectively reduce the total number of infected population.