Certain respiratory tract infections can be transmitted by hand-to-mucous-membrane contact, inhalation, and/or direct respiratory droplet spray. In a room occupied by a patient with such a transmissible infection, pathogens present on textile and nontextile surfaces, and pathogens present in the air, provide sources of exposure for an attending health-care worker (HCW); in addition, close contact with the patient when the latter coughs allows for droplet spray exposure. We present an integrated model of pertinent source-environment-receptor pathways, and represent physical elements in these pathways as "states" in a discrete-time Markov chain model. We estimate the rates of transfer at various steps in the pathways, and their relationship to the probability that a pathogen in one state has moved to another state by the end of a specified time interval. Given initial pathogen loads on textile and nontextile surfaces and in room air, we use the model to estimate the expected pathogen dose to a HCW's mucous membranes and respiratory tract. In turn, using a nonthreshold infectious dose model, we relate the expected dose to infection risk. The system is illustrated with a hypothetical but plausible scenario involving a viral pathogen emitted via coughing. We also use the model to show that a biocidal finish on textile surfaces has the potential to substantially reduce infection risk via the hand-to-mucous-membrane exposure pathway.