On modelling airborne infection risk

Airborne infection risk analysis is usually performed for enclosed spaces where susceptible indi- viduals are exposed to infectious airborne respiratory droplets by inhalation. It is usually based on exponential, dose-response models of which a widely used variant is the Wells-Riley (WR) model. We revisit this infection-risk estimate and extend it to the population level. We use an epidemiolog- ical model where the mode of pathogen transmission, airborne or contact, is explicitly considered. We illustrate the link between epidemiological models and the WR and the Gammaitoni and Nucci models. We argue that airborne infection quanta are, up to an overall density, airborne infectious respiratory droplets modified by a parameter that depends on biological properties of the pathogen, physical properties of the droplet, and behavioural parameters of the individual. We calculate the time-dependent risk to be infected for two scenarios. We show how the epidemic infection risk de- pends on the viral latent period and the event time, the time infection occurs. Infection risk follows the dynamics of the infected population. As the latency period decreases, infection risk increases. The longer a susceptible is present in the epidemic, the higher its risk of infection for equal exposure time to the mode of transmission is.