Abstract:

To study the effects of individual diffusion and spatial heterogeneity on the transmission of syphilis, we construct a heterogeneous spatial reaction diffusion model of syphilis. Firstly, the well posed problem of the model is studied, including the global existence of the solution, the dissipativity of the system and the existence of the attractor for the semiflow; Secondly, based on the definition of the next generation regeneration operator, we derive the functional expression of the basic regeneration number $R_0$; Thirdly, we discussed the dynamical behaviors of the solution regarding the threshold-$R_0 $, specifically, when $R_0>1$, the disease-free steady state is globally stable, when $R_0>1 $, the system is uniformly persistent. In special cases, we also prove the existence, uniqueness, and global stability of the positive equilibrium of the system. Finally, the theoretical results were validated and the influence of spatial factors on the transmission of syphilis was analyzed through numerical simulation. Our numerical results indicate that: (1) strengthening the treatment of early latent syphilis carriers can effectively reduce the risk of syphilis transmission among population; (2) Ignoring spatial heterogeneity will underestimate the epidemic trend of syphilis. In addition, the impact of individual diffusion rate on the transmission of syphilis cannot be ignored.

Key words: Syphilis, Reaction-diffusion model, Spatial heterogeneity, Basic reproduction number, Threshold dynamics, Numerical simulation