The Wells-Riley model is a simple model of the airborne transmission of infectious diseases, developed by William F. Wells and Richard L. Riley for tuberculosis and measles. Wells-Riley can also be applied to other diseases transmitted in the air, such as COVID-19. The model describes the situation where one or more infected people are sharing a room (and so the room air) with other people who are susceptible to infection. It makes predictions for the probability that a susceptible person becomes infected. The prediction is that infection is more likely for small poorly ventilated rooms, and if the infected person is highly infectious. 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.
Description of model Wells-Riley assumes that the air contains doses of the infectious bacterium or virus, and that you become infected if you breathe one dose in, i.e., the probability a person becomes infected, P i {\displaystyle P_{i}} , is given by
P i = probability one or more doses are inhaled {\displaystyle P_{i}={\mbox{probability one or more doses are inhaled}}}
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 doses are breathed out or otherwise emitted by the infectious person into the air of the room, such that in the room there is a concentration c D O S E {\displaystyle c_{DOSE}} of these doses per unit volume of the air. If you are breathing in air at volume rate B {\displaystyle B} , then after a time t R {\displaystyle t_{R}} in the room, the
mean number of doses inhaled = c D O S E B t R {\displaystyle {\mbox{mean number of doses inhaled}}=c_{DOSE}Bt_{R}}
The Wells-Riley then relies on standard Poisson statistics which predicts for the probability of infection
P i = 1 − exp ( − c D O S E B t R ) {\displaystyle P_{i}=1-\exp \left(-c_{DOSE}Bt_{R}\right)}
after a time t R {\displaystyle t_{R}} in the room. This is just the Poisson statistics expression for the probability of one or more doses being inhaled, once we know the mean number. So the prediction is that you are more likely to become infected if the concentration of infectious doses in the room air is high, or if you spend longer in the room. The concentration of doses will tend to be high in small, poorly ventilated rooms, and smaller in larger, better ventilated rooms.
Relation of the Wells-Riley model to epidemiology 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. For transmission of COVID-19, for example, this would be how a virus breathed out by an infected person, can cross a room and be breathed in by a susceptible person. 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. However, the probability of infection predicted by the Wells-Riley model is close to the attack rate (also called secondary attack rate, and note that this 'rate' is a probability not a rate) in epidemiology. Compare the definition of P i {\displaystyle P_{i}} in this page with the definition of the attack rate.
Mechanism of transmission of infectious diseases through the air Wells-Riley is only applicable for transmission directly via the air, not via the susceptible person picking up the infectious agent from a surface (fomite transmission). 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. Breathing and speaking produce a cone of warm (body temperature), humid air that moves out into and dissipates into the room air over a distance of about one to two metres, while a sneeze, with its much faster moving air, produces air movement up to metres away. 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.
Assumptions made by the Wells-Riley model Estimating the number of inhaled doses requires more assumptions. The assumptions made by the model are essentially:
… excerpt ends here. Continue reading the full article.
