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The Wells–Riley equation for modelling airborne infection in indoor environments is incorporated into an SEIR epidemic model with a short incubation period to simulate the transmission dynamics of airborne infectious diseases in ventilated rooms. The model enables the effect of environmental factors such as the ventilation rate and the room occupancy to be examined, and allows the long-term impact of infection control measures to be assessed. A theoretical parametric study is carried out to demonstrate how changes to both the physical environment and infection control procedures may potentially limit the spread of short-incubation-period airborne infections in indoor environments such as hospitals.