Application of Whittle's stochastic threshold theorem to a chickenpox outbreak

Abstract

OBJECTIVE: To estimate the basic reproductive rate of a chickenpox outbreak, to apply the stochastic threshold theorem to estimate the probability of an outbreak occurrence and to identify preventive measures. METHODS: The study was carried out in a daycare center comprising 16 children, 13 susceptible, one infected and two children with acquired immunity by previous disease. A stochastic susceptible - infected - removed model was applied. The basic reproductive rate (R0) was estimated using the maximum likelihood method based on probability distribution for the total size of the epidemic and making an approach of almost complete epidemic. Based on R0, the theorem was applied to establish some preventive measures for preventing a chickenpox outbreak. RESULTS: Each initially infected subject produced three new cases of infection requiring minimum vaccination coverage of 62% to prevent the outbreak or to reduce in 62% the contact among members of the group or to increase in 170% removal of infected subjects. CONCLUSIONS: The stochastic threshold theorem allows to identifying measures that could be implemented to prevent and control chickenpox outbreaks. Although the distribution of the epidemic size showed similar probability of occurrence of large and small outbreaks in a typical bimodal pattern, it illustrates the uncertainty of epidemic process in small groups, requiring close detection of outbreaks in such groups.