The impact of varying class sizes on epidemic spread in a university population

A common non-pharmaceutical intervention (NPI) during the Covid-19 pandemic has been group size limits. Further, educational settings of schools and universities have either fully closed or reduced their class sizes. As countries begin to reopen classrooms, a key question will be how large classes can be while still preventing local outbreaks of disease. Here we develop and analyse a simple, stochastic epidemiological model where individuals (considered as students) live in fixed households and are assigned to a fixed class for daily lessons. We compare key measures of the epidemic - the peak infected, the total infected by day 180 and the calculated R0 - as the size of class is varied. We find that class sizes of 10 could largely restrict outbreaks and often had overlapping inter-quartile ranges with our most cautious case of classes of 5. However, class sizes of 30 or more often result in large epdiemics. Reducing the class size from 40 to 10 can reduce R0 by as much as 30%, as well as signficantly reducing the numbers infected. Intermediate class sizes show considerable variation, with the total infected varying as much as from 20% to 80% for the same class size. We show that additional in-class NPIs can limit the epidemic still further, but that reducing class sizes appears to have a larger effect on the epidemic. We do not specifically tailor our model for Covid-19, but our results stress the importance of small class sizes for preventing large outbreaks of infectious disease.