MODELING RESPIRATOR PENETRATION VALUES WITH THE BETA-DISTRIBUTION - AN APPLICATION TO OCCUPATIONAL TUBERCULOSIS TRANSMISSION

The lognormal distribution typically is used to model variability in r espirator penetration values. The lognormal model is a good descriptor where the average penetration value is low, but may be a poor descrip tor where the average penetration value is high because a significant fraction of penetration values could be predicted to exceed unity. In this regard, the beta distribution offers greater flexibility than the lognormal in modeling penetration values over the physically plausibl e interval [0,1]. The beta distribution also is shown to be mathematic ally convenient for describing the risk of airborne transmission of tu berculosis among a respirator-wearing population. Infection can occur following inhalation of respirable particles, termed droplet nuclei, c arrying viable Mycobacterium tuberculosis bacilli. Based on the expect ed number of infectious doses inhaled, the Poisson probability model t raditionally is used to predict an individual's risk of infection. Thi s article synthesizes the beta distribution, as applied to average pen etration values among a respirator-wearing population, and the Poisson distribution, as applied to an individual's infection risk, to descri be the population risk of M. tuberculosis infection.