Modeling the Impact of Time to Treatment on Syphilis Prevalence: A Theoretical Mathematical Model of People Living With HIV in Colombia

Abstract

Background: Syphilis disproportionately affects people living with HIV (PLWH). Although screening is widely done for syphilis control, there are significant delays with time to treatment reaching 30 days in some settings in Colombia. Our study aimed to model the impact of reducing time to treatment on syphilis prevalence among PLWH in Colombia.

Methods: We developed a compartmental model to simulate syphilis transmission dynamics among PLWH, considering different stages of disease. The model included screening and treatment pathways and stratified the population into high (10%) and low (90%) sexual activity groups. Sensitivity analysis assessed the influence of various model parameters on the impact of reducing time to treatment.

Results: The model projected a syphilis prevalence of 7.7% in the base scenario, with increased prevalence in high versus low sexual activity groups (41.5% and 4.0%, respectively). Reducing the average time to treatment from 30 days to 1 day decreased the syphilis prevalence to 6.5%, or 7.1% when applied, respectively, to the entire population or only the high sexual activity group. Sensitivity analysis showed that reducing time to treatment to 1 day in 20% of the high activity group resulted in relative reductions ranging from -1.1% to -13.2% in syphilis prevalence, depending on parameter variations.

Conclusions: This study highlights the potential for reducing time to treatment to lower syphilis prevalence among PLWH. The findings emphasize the importance of targeted strategies in syphilis control efforts and underscore the complex interactions of model parameters influencing the impact of such interventions.