Fig. 1.

Schematic diagram of the individual-based model's structure for the natural history of syphilis and its testing and treatment cascade. Where ${\mu }_a$ is the age-specific all-cause mortality rate; ${\lambda }_t$ is the individual's probability of infection; $p^{import}$ is the probability of importing syphilis from another community; ${\sigma }_{i\in (1,2,..,7)}$ is duration of each syphilis disease stage; ${\varphi }^{recurrent}$ is the proportion of early latent cases that progress through the recurrent stage; ${\psi }_{a,t,s}^{test}$ is the probability of testing for syphilis, which varies by age, time, and sex; ${\varsigma }_k$ is the sensitivity of the conventional syphilis testing assay for each disease stage k; ${\pi }^{treatment}$ is the probability that treatment is successful; and ${\tau }_{i\in (1,2)}$ is the duration of treatment for patients initiated at different syphilis disease stage.