Data

The data used in this paper were collected at a US high school during one school day using wireless sensor technology. In total, 789 individuals (94% of the school population) participated. They wore small sensors that detect and record radio signals broadcast by other nearby sensors. Further, stationary devices broadcasting signals were attached to fixed locations (at least one per room) throughout the school campus to keep track of the participants’ locations.

Consequently, the data include two types of records. Close proximity interactions (CPIs) are records that indicate two participating individuals standing face-to-face with a distance of less than three meters at a certain point in time. Location records are records that indicate the presence of an individual nearby a stationary device (location information is at the level of rooms).

A detailed description on how information and noise were separated in the data is provided elsewhere18. Data were collected at time intervals of 20 seconds.

Model of influenza spread

We used an individual-based model with a susceptible, exposed, infectious, recovered (SEIR)-type structure. We assumed that influenza is introduced into the school population by one index case at the beginning of a simulation run and that no further introductions from outside occur. The duration of a simulation time step was half a day (i.e., contact information was aggregated at this level, which was shown to be a reasonable approximation for full-resolution networks27; also note that the temporal resolution of the model of virus particle air concentrations was kept at 20 seconds and only exposure levels were aggregated at the this level, see also below). Infection transmission could only occur during the half-day including school, not during the half-day including the night. Individual j’s probability P j to switch from the susceptible to the exposed state depends on the mode of transmission. We defined one function P a,j for aerosol transmission and one function P cc,j for close-contact transmission, as laid out below. We ran simulations for an all-aerosol scenario, for an all-close-contact scenario, and one for a scenario where both aerosol and close-contact transmission occur as 0.5P a,j + 0.5P cc,j . The duration of the exposed state follows a Weibull distribution with an offset of half a day; the power parameter is 2.21, the scale parameter is 1.1017,28). After that period in the exposed state, every individual will be in the infectious state for exactly one time step before turning into home confinement and, finally, recovering. To allow for the fact that the onset of influenza symptoms is typically sudden and that affected individuals will be dismissed quickly, we reduced P j by 75%, as described in Salathé et al.17, which also contains more details on all parameter choices other than those specific to the aerosol transmission probability.

Close-contact transmission probability

Assumptions, parameters, and structure of the close-contact transmission model are described in detail elsewhere17, and therefore only described briefly here.

Close-contact transmission requires social interaction between an infectious and a susceptible individual, and it includes transmission via large droplets that do not travel far and do not stay suspended in the indoor air as well as transmission via direct, physical contact29. Risk of transmission is usually operationalized as a function of contact duration30. Based on data from an outbreak on a commercial airliner31, the probability of transmission was estimated as

$${P}_{cc,j}=1-{(1-0.003)}^{T}$$ (1)

with T being the contact duration between two individuals in number of sensor recordings (every 20 s)17.

Aerosol transmission probability

In our model, we quantify amounts of aerosolized virus particles in ‘quanta’, following Wells’32 quantum theory of disease transmission. A quantum is defined as the amount of infectious droplet nuclei required to infect the fraction 1 − 1/e of a susceptible population exposed to it.

We assume that every room of the school is a well-mixed airspace that is only connected to the outside, but does not exchange air with other rooms. We further assume that removal of aerosolized virus particles by ventilation is the dominant removal process and that, e.g., neither inactivation nor settling play an important role at low levels of relative humidity typical for influenza season (which is a standard assumption in the literature, cf., e.g.22,33). Under these assumptions, we model the concentration of virus particles in a particular room r as

$$\frac{{\rm{\Delta }}{C}_{r,t}}{{\rm{\Delta }}t}=\frac{{\sum }_{i\in {I}_{r,t}}{q}_{i,t}}{{V}_{r}}-{C}_{r,t}\frac{{Q}_{r,t}}{{V}_{r}}$$ (2)

where C r,t is the quanta concentration in room r at time t, I r,t is the set of all infectious individuals that are in room r at time t, q i,t is the quanta shedding rate of infector i at time t, V r is the volume of room r, and Q r,t is the fresh air supply rate of room r at time t. The quotient Q r,t /V r is also known as the air change rate (ACR).

The instantaneous dose of infectious material, D j,t , inhaled by individual j at time step t is given by

$${D}_{j,t}={C}_{r,t}{p}_{j}{\rm{\Delta }}t$$

where C r,t is the quanta concentration in room r - the room in which individual j is located at time t - at time t, p j is the breathing rate of individual j, and Δt is the duration of a simulation time step, here 20 s.

Individual j’s total exposure, D j during an entire school day is given by

$${D}_{j}={\sum }_{t={t}_{0}}^{{t}_{x}}{D}_{j,t}.$$

Combining the total daily exposure with Wells’ definition of quanta allows to model the probability P a,j of a fully susceptible individual to become infected during one simulation school day as

$${P}_{a,j}=1-\exp (\,-\,{D}_{j})$$ (3)

where the total exposure D j is the only parameter required.

Shedding rate: Both bottom-up3,34 and top-down approaches35 have been used by others to estimate quanta-based shedding rates for influenza. Bottom-up studies (mechanistic approaches starting from basic measurements and processes) suffered from huge uncertainties and differed by three orders of magnitude. We used data from Rudnick and Milton’s35 top-down study that back-calculated quanta shedding rates from the same outbreak data31 that was also used to parameterize the close-contact model17. They estimated shedding rates of between 79 quanta/h and 128 quanta/h, depending on model assumptions. We chose a shedding rate of 100 quanta/h for our aerosol transmission model.

Ventilation rate: We assumed different scenarios for the ventilation rate. According to the ventilation recommendations for schools by the American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE)21, the ventilation rate for classrooms should be at least 8 l/s per person. Daisey et al.36 estimate that for a typical classroom situation, this corresponds to an air change rate (ACR) of 3.0 air changes per hour. This estimate served as our good-ventilation scenario. Various studies found substantially lower ACR in US schools36,37,38, and CO 2 concentrations at the high school we collaborated with (unpublished data) indicated very poor ventilation conditions, too. In line with reported ACR in other US schools, we assumed 0.5 air changes per hour for a poor ventilation scenario. Additionally, we used 1.5 air changes per hour as a middle scenario.

Breathing rate: The breathing rate of humans depends mainly on their age, gender, and activity levels39. In line with Adams’39 measurements and in accordance with other work in the field35, we assumed a constant breathing rate of 8 l/min for every individual.

Interventions

We compared ventilation-based interventions (effect only on aerosol transmission) with vaccinating individuals (effect independent on transmission pathway).

Ventilation rate: Baseline scenario to which all intervention scenarios were compared with was the poor ventilation scenario (ACR 0.5 h−1). Basic interventions were improving the ventilation to ASHRAE standards (ACR 3.0 h−1) and to achieve an intermediate improvement (ACR 1.5 h−1), respectively.

We further analyzed how ventilation improvement only in some rooms would affect infection spread. We defined three different methods to identify rooms for which the ACR was increased from 0.5 h−1 to 3.0 h−1: (i) optimal, using all available information from simulation runs, we identified rooms with the highest cumulative exposure, i.e., where most susceptibles will be exposed or where doses are highest in a typical simulation run; (ii) schedule-based, identifying rooms with the highest cumulative occupancy throughout a school day according to the school’s official roster; (iii) size-corrected, which is similar to the schedule-based approach, but the total occupancy was divided by the volume of the room to give priority to small rooms with a high occupancy, as quanta concentration builds up faster in small rooms.

All three methods were used to identify rooms that represent 5%, 10%, 15%, 20% and 25% of the total indoor space. Methods (ii) and (iii) could realistically be applied in a school setting. Comparing interventions based on them with optimal ones allows assessing their relative performance to the theoretical optimum.

Vaccination: We assumed a vaccination effectiveness (protection against transmission) of 60%26 as a standard scenario (In sensitivity analyses we also assumed 40% and 80%) and a random distribution of vaccination status among the school population. We simulated the impact of vaccination for vaccination coverage values between 0% (baseline) and 100% with increments of 10%.

Ethical approval

All measurements involving human subjects were conducted according to the relevant regulations and involved an informed consent obtained from all subjects. The whole study was previously approved by the Stanford IRB (Institutional Review Board).

Accession codes

The data code to reproduce results and figures are available on a GitHub repository at https://github.com/salathegroup/aerosol. The input files needed to reproduce the computer simulations can be found in a dedicated folder at https://github.com/salathegroup/aerosol/tree/master/input_files.