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 ventilationwould 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 .
We develop a spatially dependent generalisation to the Wells-Riley model and its extensions applied to COVID-19 , that determines the infection risk due to airborne transmission of viruses. We assume that the concentration of infectious particles is governed by an advection-diffusion-reaction equation with the particles advected by airflow, diffused due to turbulence, emitted by infected people and removed due to the room ventilation, inactivation of the virus and gravitational settling. We consider one asymptomatic or presymptomatic infectious person who breathes or talks, with or without a mask and model a quasi-3D setup that incorporates a recirculating air-conditioning flow. A semi-analytic solution is available and this enables fast simulations. We quantify the effect of ventilation and particle emission rate on the particle concentration, infection risk and the `time to probable infection' (TTPI). Good agreement with CFD models is achieved. Furthermore, we derive power laws that quantify the effect of ventilation, emission rate and infectiousness of the virus on the TTPI. The model can be easily updated to take into account modified parameter values. This work paves the way for establishing `safe occupancy times' at any location and has direct applicability in mitigating the spread of the COVID-19 pandemic .
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Due to the rate at which the
We develop a spatially dependent generalisation to the Wells-Riley model and its extensions applied to
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pandemic is spreading, a model for indoors airborne transmission that is quick to implement is required. We create such a model assuming
,
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determines the infection risk due to airborne transmission of viruses. We assume that
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airborne
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. 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
with the particles advected by airflow, diffused due to turbulence, emitted by infected people and removed due to the room ventilation, inactivation of the virus and gravitational settling. We consider one asymptomatic or presymptomatic infectious person who breathes or talks, with or without a mask and model a quasi-3D setup that incorporates a recirculating air-conditioning flow. A semi-analytic solution is available and this enables fast simulations. We quantify the effect of ventilation and particle emission rate on the particle concentration, infection risk and
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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 ventilationwould 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
`time to probable infection' (TTPI). Good agreement with CFD models is achieved. Furthermore, we derive power laws that quantify the effect of ventilation,
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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
infectiousness of the virus on the TTPI. The model can be easily updated to take into account modified parameter values. This work paves the way for establishing `safe occupancy times' at any location and has direct applicability in mitigating the spread of the COVID-19 pandemic