A mathematical model of three-dimensional transport of gas-phase contaminants in indoor environments based on a Markov chain, the Markov model, was extended to solid-phase contaminant transport in indoor environment. The performance of the model was affirmed by comparison with simplified transport models, and a previously published study of poly-dispersed particulate transport in a quiescent environment. I conducted an experiment to measure the transport and fate of mono-dispersed fluorescein-tagged particles with nominal aerodynamic diameters of 3 μm and 14 μm under turbulent and quiescent conditions in a room-scale chamber. Advection and turbulence were characterized using 3-axis anemometery and tracer gas studies. Parameterization of turbulence in the Markov model was explored: Turbulent diffusion coefficients and fluctuating velocities were associated with mixing time through simulation, but the simulated fluctuating velocities were not strongly correlated with measured fluctuating velocities. The Markov model did not replicate the experimental results with high fidelity, but this may be due in part to limitations in the anemometry, and the complexity of the aerosol release. The public health significance of the mathematical modeling was demonstrated in the context of Mycobacterium tuberculosis exposure and infection risk in commercial passenger aircraft. Infection risk to passengers, and the impact of exposure reduction strategies were quantitatively assessed using the Markov model in conjunction with Monte Carlo simulation. The expected infections ranged from 10 ^-6 to 10^-1 per 169 susceptible passengers, for an exponential (k = 1) dose-response function. Use of respiratory protection, surgical masks or filtering facepiece respirators, by the infectious source and/or the susceptible passengers reduced infection risk by a factor of 2-10.