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The classical deterministic susceptible-infectious-recovered (SIR) model has played an important role in the analysis of epidemic systems with large populations. However, when population numbers become small e.g. in a hospital ward, a stochastic analysis will be vital. The stochastic Petri-Nets using Gillespie algorithm for modeling the transmission of airborne infections in enclosed spaces is present to be incorporated into an SIR epidemic model with a short incubation period to simulate the transmission dynamics of airborne infectious diseases in indoor environments. The stochastic model not only allows the long-term impact of infection control measures and enables the evaluation of environmental factors, but also depicts the probability of an outbreak of an airborne infection. A quantitative performance study was carried out to demonstrate how to limit the probability rate of outbreak of infection.