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Since 1927, until recently, models describing the spread of disease havemostly been of the SIR-compartmental type, based on the assumption thatpopulations are homogeneous and well-mixed. The focus of these models havetypically been on large-scale analysis of scenarios such as cities, nations oreven world scale. SIR models are appealing because of their simplicity, buttheir parameters, especially the transmission rate, are complex and depend on anumber of factors, which makes it hard to predict how a change of a singleenvironmental, demographic, or epidemiological factor will affect thepopulation. Therefore, in this contribution we start to unpick thetransmission-rate parameter. Analysing the implications that arise when takingcrowd behaviour explicitly into account, we show how both the rate of infectionas well as the walking speed depend on the local crowd density around aninfected individual. The combined effect is that the rate of infection at apopulation scale has an analytically tractable non-linear dependency on crowddensity. We model the spread of a hypothetical disease in a corridor andcompare our new model with a typical compartmental model, which highlights theregime in which current models may not produce credible results.

Analytical Modelling of the Spread of Disease in Confined and Crowded Spaces