An age-structured syphilis model, II: optimal control and numerical simulation

The World Health Organization estimated that 8 million adults between 15 and 49 years old acquired syphilis globally in 2022. China CDC reported that there were 530 116 cases of syphilis in mainland China in 2023. Since syphilis is a sexually transmitted disease and age structure of the host population plays a crucial role, in this series of two papers we develop an age-structured model with four infection stages (primary, secondary, latent and tertiary) to study the transmission dynamics of syphilis. In part I (Wu et al . 2025 Proc. R. Soc. A 481 : 20240218 (doi: 10.1098/rspa.2024.0218 )), we investigated the well-posedness of the model and studied stability of the steady states. In part II, first, we consider the optimal control of the age-structured model. Second, utilizing the Markov Chain Monte Carlo method, we calibrate the reported syphilis data in China by using a demographic model. 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); (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 populations.