  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.
