Markov modeling of contaminant concentrations in indoor air

Most models for contaminant dispersion in indoor air are deterministic and do not account for the probabilistic nature of the pollutant concentration at a given room position and time. Such variability can be important when estimating concentrations involving small numbers of contaminant particles. This article describes the use of probabilistic models termed Markov chains to account for a portion of this variability. The deterministic and Markov models are related in that the former provide the expected concentration values. To explain this relationship, a single-zone (well-mixed room) scenario is described as a Markov chain. Subsequently, a two-zone room is cast as a Markov model, and the latter is applied to assessing a health care worker's risk of tuberculosis infection. Airborne particles carrying Mycobacterium tuberculosis bacilli are usually present in small numbers in a room occupied by an infectious tuberculosis patient. For a given scenario, the Markov model permits estimates of variability in exposure intensity and the resulting variability in infection risk.