Deterministic SIR (Susceptible–Infected–Removed) models applied to varicella outbreaks

Abstract

Deterministic SIR models were applied to simulate Susceptible-Infected-Removed and to estimate the threshold condition for varicella outbreaks in children, reported in Medellín, Colombia. The expected numbers of susceptible, infected and removed individuals were compared with observed cases from notification of varicella outbreaks to the local Board of Health and from survey data. The threshold condition was estimated by the basic reproductive ratio and by the relative removal rate, through which measures for preventing and curtailing the outbreaks were identified. The model demonstrated a reasonable fit to the observations, except in two of the six outbreaks which probably reflected under-registration of cases. In order to have prevented these outbreaks, between 4.4% and 52.9% of the susceptible population should have been vaccinated assuming an 85% vaccine effectiveness. Similarly, isolation of affected children should have been increased to between 4.3% and 44.8% per week.