# What could re-infection tell us about R0? a modeling case-study of syphilis transmission

## TL;DR

This study explores how re-infection rates relate to the basic reproductive number (R0) in infectious diseases, using a model of syphilis transmission to inform epidemic control strategies.

## Contribution

The paper derives an analytic expression linking re-infection proportion to R0 and validates it with numerical simulations for syphilis.

## Key findings

- Re-infection proportion increases monotonically with R0
- The relationship is affected by entry/exit rates and treatment
- Re-infection rates can serve as indicators for epidemic control

## Abstract

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.

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Source: https://tomesphere.com/paper/1903.05984