Abstract
A common non-pharmaceutical intervention (NPI) during the COVID-19 pandemic has been group size limits. Furthermore, 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 five. However, class sizes of 30 or more often result in large epidemics. Reducing the class size from 40 to 10 can reduce R0 by over 30%, as well as significantly reducing the numbers infected. Intermediate class sizes show considerable variation, with the total infected varying by as much as from 10% 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.
Highlights
The classic susceptible–infected–recovered (SIR) epidemiological model has long been used to model the spread of infectious disease in human, animal and plant populations [1,2]
Taking an average household size of 10 and comparing the most central 50% of runs for average class sizes of 10 and 40, it is clear that smaller class sizes substantially restrict the epidemic
A clear result from our model is that the smaller the class size, the lesser the severity of the epidemic
Summary
The classic susceptible–infected–recovered (SIR) epidemiological model has long been used to model the spread of infectious disease in human, animal and plant populations [1,2]. Pandemic has been restricting population mixing through ‘lockdowns’, with people encouraged to stay at 2 home and avoid mixing with individuals outside their household unless essential. This has often included closing educational settings of universities and schools, with 31 countries enacting full school closures and reduced schooling in a further 48 countries [7]. There have been some excellent, in-depth modelling studies of infection spread in educational settings, especially universities, with a range of NPIs included, often with a focus on testing and isolation strategies [8,9,10,11]. We focus on the question of how class sizes may impact an epidemic
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