What could re-infection tell us about R(0)? A modeling case-study of syphilis transmission

Many infectious diseases can lead to re-infection. We examined the relationship between the prevalence of repeat infection and the basic reproductive number (R(0)). First we solved a generic, deterministic compartmental model of re-infection to derive an analytic solution for the relationship. We then numerically solved a disease-specific model of syphilis transmission that explicitly tracked re-infection. We derived a generic expression that reflects a non-linear and monotonically increasing relationship between proportion re-infection and R(0) and which is attenuated by entry/exit rates and recovery (i.e. treatment). Numerical simulations from the syphilis model aligned with the analytic relationship. Re-infection proportions could be used to understand how far regions are from epidemic control, and should be included as a routine indicator in infectious disease surveillance.