Risk assessment for long and short range airborne transmission of SARS-CoV-2, indoors and outdoors

Preventive measures to reduce infection are needed to combat the COVID-19 pandemic and prepare for a possible endemic phase. Current prophylactic vaccines are highly effective to prevent disease but lose their ability to reduce viral transmission as viral evolution leads to increasing immune escape. Long term proactive public health policies must therefore complement vaccination with available nonpharmaceutical interventions (NPI) aiming to reduce the viral transmission risk in public spaces. Here, we revisit the quantitative assessment of airborne transmission risk, considering asymptotic limits that considerably simplify its expression. We show that the aerosol transmission risk is the product of three factors: a biological factor that depends on the viral strain, a hydrodynamical factor defined as the ratio of concentration in viral particles between inhaled and exhaled air, and a face mask filtering factor. The short range contribution to the risk, both present indoors and outdoors, is related to the turbulent dispersion of exhaled aerosols by air drafts and by convection (indoor), or by the wind (outdoors). We show experimentally that airborne droplets and CO$_2$ molecules present the same dispersion. As a consequence, the dilution factor, and therefore the risk, can be measured quantitatively using the CO$_2$ concentration, regardless of the room volume, the flow rate of fresh air and the occupancy. We show that the dispersion cone leads to a concentration in viral particles, and therefore a short range transmission risk, inversely proportional to the squared distance to an infected person and to the flow velocity. The aerosolization criterion derived as an intermediate result, which compares the Stokes relaxation time to the Lagrangian time scale, may find application for a broad class of aerosol-borne pathogens and pollutants.