Refining a risk model for occupational tuberculosis transmission

The traditional Poisson probability model for airborne Mycobacterium tuberculosis (M.tb) infection, also termed the Wells-Riley equation, can be modified to account for a health care worker's use of respiratory protection. It was previously shown that the beta distribution on the interval [0,1] is a good descriptor of respirator penetration values experienced by an individual worker from wearing to wearing, and of average respirator penetration values experienced by different workers. Based on the premise that the gamma distribution can reasonably describe the time-varying M.tb aerosol exposure levels experienced by health care workers, analytical solutions are presented for an individual worker's cumulative risk of infection, and for the worker population mean cumulative risk of infection, with and without use of respiratory protection. The gamma distribution is shown to be similar to the lognormal in describing right-skewed distributions of aerosol exposure concentrations on the interval [0, infinity).