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Necessity of ventilation for mitigating virus transmission quantified simply

To mitigate the SARS-CoV-2 pandemic, officials have employed social distancing and stay-at-home measures, with increased attention to room ventilation emerging only more recently. Effective distancing practices for open spaces can be ineffective for poorly ventilated spaces, both of which are commonly filled with turbulent air. This is typical for indoor spaces that use mixing ventilation. While turbulence initially reduces the risk of infection near a virion-source, it eventually increases the exposure risk for all occupants in a space without ventilation. To complement detailed models aimed at precision, minimalist frameworks are useful to facilitate order of magnitude estimates for how much ventilation provides safety, particularly when circumstances require practical decisions with limited options. Applying basic principles of transport and diffusion, we estimate the time-scale for virions injected into a room of turbulent air to infect an occupant, distinguishing cases of low vs. high initial virion mass loads and virion-destroying vs. virion-reflecting walls. We consider the effect of an open window as a proxy for ventilation. When the airflow is dominated by isotropic turbulence, the minimum area needed to ensure safety depends only on the ratio of total viral load to threshold load for infection. The minimalist estimates here convey simply that the equivalent of ventilation by modest sized open window in classrooms and workplaces significantly improves safety.