Predicting the spatio-temporal infection risk in indoor spaces using an efficient airborne transmission model.

We develop a spatially dependent generalization to the Wells-Riley model, which determines the infection risk due to airborne transmission of viruses. We assume that the infectious aerosol concentration is governed by an advection-diffusion-reaction equation with the aerosols advected by airflow, diffused due to turbulence, emitted by infected people, and removed due to ventilation, inactivation of the virus and gravitational settling. We consider one asymptomatic or presymptomatic infectious person breathing or talking, with or without a mask, and model a quasi-three-dimensional set-up that incorporates a recirculating air-conditioning flow. We derive a semi-analytic solution that enables fast simulations and compare our predictions to three real-life case studies-a courtroom, a restaurant, and a hospital ward-demonstrating good agreement. We then generate predictions for the concentration and the infection risk in a classroom, for four different ventilation settings. We quantify the significant reduction in the concentration and the infection risk as ventilation improves, and derive appropriate power laws. The model can be easily updated for different parameter values and can be used to make predictions on the expected time taken to become infected, for any location, emission rate, and ventilation level. The results have direct applicability in mitigating the spread of the COVID-19 pandemic.

Vitrifying multiple embryos in different arrangements does not alter the cooling rate.

Vitrification is the most common method of cryopreservation of gametes in fertility clinics due to its improved survival rates compared to slow freezing techniques. For the Open Cryotop® vitrification device, the number of oocytes, or embryos, mounted onto a single device can vary. In this work, a mathematical model is developed for the cooling of oocytes and embryos (samples). The model is solved computationally, to investigate whether varying the number of samples mounted onto the Open Cryotop® affects the cooling rates, and consequently the survival rates, of vitrified samples. Several realistic spatial arrangements of samples are examined, determining their temperature over time. In this way we quantify the effect of spatial arrangement on the cooling rate. Our results indicate that neither the spatial arrangement nor the number of mounted samples has a large effect on cooling rates, so long as the volume of the cryoprotectant remains minimal. The time taken for cooling is found to be on the order of half a second, or less, regardless of the spatial arrangement or number of mounted samples. Hence, rapid cooling can be achieved for any number or arrangement of samples, as long as device manufacturer guidelines are adhered to.