  Many infectious diseases can lead to re-infection. We examined the
relationship between the prevalence of repeat infection and the basic
reproductive number (R0). 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 R0 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.
