The transport and fate of human expiratory droplets play a key role in the transmission of respiratory infectious diseases. In this paper, we present a modeling approach to understand the fundamental dynamics of exhaled droplets in human respiratory activities. The model solves a series of governing equations of droplets and uses a continuous random walk model to simulate turbulent fluctuations in violent expiratory events. The validation of the model shows the improvement in the prediction of dispersion of median-sized droplets. We show that these droplets are sensitive to environmental conditions, including temperature, humidity, and ambient flows. Applying the model to a set of idealized conditions such as free-fall and continuous jets, we demonstrate significantly different impacts of environmental parameters on droplets with different sizes. Using a realistic droplet size distribution and cough duration, we quantify the transport and fate of droplets in the near field of source and the potential influences by ambient conditions. The model we developed from this study could be applied to study the mechanisms for airborne pathogens, e.g., influenza virus and new coronavirus.
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