  Due to the rate at which the COVID-19 pandemic is spreading, a model for
indoors airborne transmission that is quick to implement is required. We create
such a model assuming that the concentration of airborne infectious particles
is governed by an advection-diffusion-reaction equation. As schools and
universities are intensively discussing how to operate their indoor spaces, we
solve the model for a classroom, assuming one infectious person at the centre
of the room and quantify the effect of several ventilation settings when the
person is breathing or talking, both with and without a face mask. We compare
our model with more complex models and with experimental data and find good
agreement. The framework can be easily applied to any other high-risk location.
We also generate maps of the Time To Infection (TTI) by airborne transmission,
for various activities and ventilation levels. Using the TTI maps we quantify
the airborne transmission risk and make recommendations for the Safe Occupancy
Time (SOT), for a chosen risk tolerance level. As expected, we find that the
SOT decreases with ventilation quality. We also establish the recommended
"vacancy time" after an activity in the room. For example, to achieve an
airborne transmission risk of less than 5%, the pre-pandemic ASHRAE recommended
ventilation would allow 37-minute lessons followed by 35-minute breaks but if
the ventilation is poor, 25-minute lessons should be followed by 166-minute
breaks. Our model also uncovers power-law relationships for the concentration
as a function of time and particle emission rate and for the TTI as a function
of ventilation rate and particle emission rate; these may be used as a fast
tool to predict the SOT in several realistic scenarios. Finally, we show that
wearing a mask of 50% efficiency could increase the SOT by 98% and reduce the
vacancy time by up to 55%, depending on the ventilation setting.
