Abstract
A mathematical model to describe the population of airborne bacteria in an enclosed space has been derived. The derivation is based on a stochastic immigration and death process with two assumptions: (a) The population is relatively uniform throughout the enclosed space, and (b) the population at a given point varies in a random manner primarily owing to air turbulence. Three distinct situations are considered in the presentation. The first is a region of finite time where the mean concentration in the space is increasing owing to generation within the space. A second situation involves a region with constant mean concentration as time approaches infinity. The third situation is one in which generation within the space has stopped and the mean concentration decreases to zero. The mathematical model has been verified by generating a population of airborne bacteria within an enclosed space and continuous monitoring of the concentration by air sampling. Parameters such as aerosol generation rate, ventilation rate of the space, settling rate of the aerosol particles, and die-away characteristics of the aerosol are accounted for.