Is well-mixed model of an indoor space with ceiling fans valid for studying pathogen transmission?

Airborne transmission is one of the main modes for the transmission of highly infectious diseases such as COVID-19. Pathogen laden aerosols from an infected person can be transported by air to a susceptible population. A widely used model for airborne transmission considers the indoor space to be well-mixed such that the pathogen concentration is spatially homogeneous. Other models that employ computational fluid dynamics (CFD) allow tracking the spatiotemporal variation of infection probability in indoor spaces but are computationally expensive. Here, we compare the predictions of a well-mixed continuously stirred tank reactor (CSTR) model for indoor transmission with CFD for airflow, along with the Lagrangian tracking of aerosol particles. Of particular interest is the ventilation using ceiling fans, which are common in South East Asia. It is found that the behavior of particles at the walls plays an important role. Two limiting cases are studied: all particles reaching the wall get trapped vs all particles being reflected from the solid boundaries. We propose a modification to the CSTR equation to include the wall effect, and it matches the CFD data closely.