The Wells-Riley model is a simple model of the airborne transmission of infectious diseases,[1][2] developed by William F. Wells and Richard L. Riley for tuberculosis[3] and measles.
It makes predictions for the probability that a susceptible person becomes infected.
The Wells-Riley is a highly simplified model of a very complex process, but does at least make predictions for how the probability of infection varies with things within our control, such as room ventilation.
This dose is not a single bacterium or virus, but however many are needed to start an infection.
These infectious doses are sometimes called 'quanta' - no relation to quantum physics.
The Wells-Riley then relies on standard Poisson statistics which predicts for the probability of infection
This is just the Poisson statistics expression for the probability of one or more doses being inhaled, once we know the mean number.
Note that the Wells-Riley model approaches transmission of an airborne diseases as a physical transport problem, i.e., as the problem of how a virus or bacterium gets from one human body to another.
This is a different approach from that taken in the epidemiology of infectious diseases, which may gather information about who (e.g., nurses, factory workers) becomes infected, in what situations (e.g., the home, factories), and understand the spread of a disease in those terms - without considering how a virus or bacterium actually gets from one person to another.
[1] Because the model assumes the air is well mixed it does not account for the region within one or two metres of an infected person, having a higher concentration of the infectious agent.
[9] If the person breathing/speaking/sneezing is infected then an infectious agent such as tuberculosis bacterium or a respiratory virus is expected to be more concentrated in this cone of air, but the infectious agent can also (at least in some cases) spread into the room air.
[10] Estimating the number of inhaled doses requires more assumptions.
Doses can be removed in three ways: Assuming we can add the rates of these processes
the lifetime of a dose in the air before settling onto a surface or the floor, and
the lifetime of the dose before it is removed by room ventilation or filtration.
inside the room and inhales air at a rate (volume per unit time)
{\displaystyle {\mbox{mean number of inhaled doses}}={\frac {r_{DOUT}Bt_{R}}{V_{ROOM}\left(1/\tau _{D}+1/\tau _{F}+1/\tau _{VF}\right)}}}
is just one over the air changes per hour - one measure of how well ventilated a room is.
Building standards recommend several air changes per hour, in which case
The Wells-Riley model assumes that an infected person continuously breathes out infectious virus.
The excess concentration of carbon dioxide is that over the background level in the Earth's atmosphere, which is assumed to come from human respiration (in the absence of another source such as fire).
Carbon dioxide neither sediments out (it is a molecule) nor decays, leaving ventilation as the only process that removes it.
times the concentration of carbon dioxide in exhaled breath
Although originally developed for other diseases such as tuberculosis, Wells-Riley has been applied[5][14] to try and understand transmission of COVID-19, notably for a superspreading event in a chorale rehearsal in Skagit Valley (USA).
The probability of becoming infected is predicted to increase with how infectious the person is (
- which may peak around the time of the onset of symptoms and is likely to vary hugely from one infectious person to another,[2][16] how rapidly they are breathing (which for example will increase with exercise), the length of the time they are in the room, as well as the lifetime of the virus in the room air.
This lifetime can be reduced by both ventilation and by removing the virus by filtration.
Large rooms also dilute the infectious agent and so reduce risk - although this assumes that the air is well mixed - a highly approximate assumption.
[2][8][10] A study of a COVID-19 transmission event in a restaurant in Guangzhou, went beyond this well-mixed approximation, to show that a group of three tables shared air with each other, to a greater extent than with the remainder of the (poorly ventilated) restaurant.
The COVID-19 pandemic has led to work on improving the Wells-Riley model to account for factors such as the virus being in droplets of varying size which have varying lifetimes,[18] and an improved model[18] also has an interactive app.