Classical mathematical epidemiology has highlighted the need to identify a critical population size for an epidemic to drive across a community. This threshold depends not only on the nature of the epidemic but also on the scale of the available susceptible population. Clearly if few are susceptible, as is the case within an immunised community, there can be no epidemic. However if the immunisation rate drops below a certain level, the number susceptible increases and localised, minor epidemics can break out in schools, nursing homes or other vulnerable community settings.
In the early stages of a new epidemic where no vaccine is available all persons are susceptible. As the epidemic progresses and the number of infectious individuals increases the number of susceptible individuals will decrease. However when an epidemic can produce both asymptomatic and symptomatic cases the identification of the numbers infected becomes more challenging. Yet it is the estimates of this very number that is required to enable decisions on when a community has reached its critical threshold point and when policy makers and planners can advise on school openings, safety for nursing homes and protection of the vulnerable communities.
Mathematical and statistical models of back-calculation have been used successfully both internationally and in Ireland to produce estimates of the scale of a hidden infected population within HIV/AIDS, heroin use and more recently bio-terrorism, where the comparatively short incubation periods are particularly applicable to Covid-19. Working with observed symptomatic cases and the known incubation period, these models predict through the incubation period distribution the total numbers of infected and asymptomatic cases these observed cases arose from. Using back-calculation methods with reporting delays, age structure and a range of models for the observable cases, this study will provide crucial estimates for planners of the scale of the asymptomatic Covid-19 population.
