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

TL;DR

This paper develops an analytical model for disease spread in crowded spaces that explicitly accounts for crowd behavior, revealing non-linear dependencies of infection rate on crowd density, and compares it with traditional SIR models.

Contribution

It introduces a new analytical model incorporating crowd density effects into disease transmission, addressing limitations of traditional homogeneous population models.

Findings

Infection rate depends non-linearly on crowd density.

Model shows regimes where traditional models may fail.

Comparison highlights differences in predicted spread.

Abstract

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.