Spatiotemporal dynamics of syphilis in Xinjiang via a demographic-geographic data-validated reaction diffusion model

To explore the spatiotemporal transmission dynamics of syphilis in Xinjiang Province, we establish a multi-stage infection syphilis reaction-diffusion model that incorporates demographic and geographic data. The well-posedness of the system is studied. Then, we derive the basic reproduction number R0, which serves as the critical threshold for disease outbreak or extinction. We also prove the global dynamics of the homogeneous model parameters and heterogeneous diffusion coefficients case by constructing the feasible Lyapunov functional. Finally, based on data from Xinjiang Province from 2004 to 2018, we estimate model parameters via the Markov Chain Monte Carlo method. The effects of treatment and intervention measures on syphilis spread are explored from both one-dimensional and two-dimensional perspectives. One-dimensional numerical simulations validate the theoretical results and show that increasing treatment coverage and strengthening public health interventions reduce syphilis infections. A two-dimensional simulation of syphilis transmission is conducted using COMSOL Multiphysics software and the finite element method, incorporating Xinjiang Province’s population and geographic data to capture regional differences. Our results suggest: (1) Syphilis infection is more severe in the southern region of Xinjiang Province than in the northern region. (2) Syphilis treatment measures in Xinjiang Province should be tailored to local conditions. Specifically, syphilis prevention efforts should focus on enhancing local healthcare and public awareness, while addressing regional disparities through tailored control strategies in Xinjiang Province.