Mathematical Assessment of the Role of Early Latent Infections and Targeted Control Strategies on Syphilis Transmission Dynamics

A new multi-stage deterministic model for the transmission dynamics of syphilis, which incorporates disease transmission by individuals in the early latent stage of syphilis infection and the reversions of early latent syphilis to the primary and secondary stages, is formulated and rigorously analysed. The model is used to assess the population-level impact of preventive (condom use) and therapeutic measures (treatment using antibiotics) against the spread of the disease in a community. It is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the associated control reproduction number (denoted by (Formula presented.)) is less than unity. A special case of the model is shown to have a unique and globally-asymptotically stable endemic equilibrium whenever the associated reproduction number (denoted by (Formula presented.)) exceeds unity. Uncertainty and sensitivity analysis of the model, using parameter values and ranges relevant to syphilis transmission dynamics in Nigeria, show that the top three parameters that drive the syphilis infection (with respect to (Formula presented.)) are the disease transmission rate ((Formula presented.)), compliance in condom use (c) and efficacy of condom ((Formula presented.)). Numerical simulations of the model show that the targeted treatment of secondary syphilis cases is more effective than the targeted treatment of individuals in the primary or early latent stage of syphilis infection.