The quantitative analysis of viral transmission risk in public places such as schools, offices, university lecture halls, hospitals, museums, theaters or shopping malls makes it possible to identify the effective levers for a proactive policy of health security and to evaluate the reduction in transmission thus obtained. The contribution to the epidemic propagation of SARS-CoV-2 in such public spaces can be reduced in the short term to a level compatible with an epidemic decline, i.e. with an overall epidemic reproduction rate below one. Here, we revisit the quantitative assessment of indoor and outdoor transmission risk. We show that the long range aerosol transmission is controlled by the flow rate of fresh air and by the mask filtering quality, and is quantitatively related to the CO2 concentration, regardless the room volume and the number of people. The short range airborne transmission is investigated experimentally using dedicated dispersion experiments performed in two French shopping malls. Exhaled aerosols are dispersed by turbulent draughts in a cone, leading to a concentration inversely proportional to the squared distance and to the flow velocity. We show that the average infection dose, called the viral quantum, can be consistently determined from epidemiological and biological experimental data. Practical implications. The results provide a rational design of sanitary policies to prevent the dominant routes of viral transmission by reinforced ventilation, air purification, mechanical dispersion by fans and incentives for correct wearing of quality masks (surgical mask, possibly covered by a fabric mask, or non-medical FFP2 masks). Combined, such measures significantly reduce the airborne transmission risk of SARS-CoV-2, with a quantitative assessment.