  Since 1927, until recently, models describing the spread of disease have
mostly been of the SIR-compartmental type, based on the assumption that
populations are homogeneous and well-mixed. The focus of these models have
typically been on large-scale analysis of scenarios such as cities, nations or
even world scale. SIR models are appealing because of their simplicity, but
their parameters, especially the transmission rate, are complex and depend on a
number of factors, which makes it hard to predict how a change of a single
environmental, demographic, or epidemiological factor will affect the
population. Therefore, in this contribution we start to unpick the
transmission-rate parameter. Analysing the implications that arise when taking
crowd behaviour explicitly into account, we show how both the rate of infection
as well as the walking speed depend on the local crowd density around an
infected individual. The combined effect is that the rate of infection at a
population scale has an analytically tractable non-linear dependency on crowd
density. We model the spread of a hypothetical disease in a corridor and
compare our new model with a typical compartmental model, which highlights the
regime in which current models may not produce credible results.
