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

Authors: Gosce, Lara; Barton, David A W; Johansson, Anders F;

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

Abstract

AbstractSince 1927 and until recently, most models describing the spread of disease have been of compartmental type, based on the assumption that populations are homogeneous and well-mixed. Recent models have utilised agent-based models and complex networks to explicitly study heterogeneous interaction patterns, but this leads to an increasing computational complexity. Compartmental 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 propose a middle ground, utilising crowd-behaviour research to improve compartmental models in crowded situations. 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.

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United Kingdom
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Keywords

name=Engineering Mathematics Research Group, 570, Physics - Physics and Society, /dk/atira/pure/core/keywords/engineering_mathematics_research_group; name=Engineering Mathematics Research Group, Populations and Evolution (q-bio.PE), FOS: Physical sciences, Physics and Society (physics.soc-ph), Environment, Models, Biological, /dk/atira/pure/core/keywords/engineering_mathematics_research_group, 630, Article, Kinetics, Crowding, FOS: Biological sciences, Infectious diseases, Humans, Disease, Statistical physics, Quantitative Biology - Populations and Evolution

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    37
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
37
Top 10%
Top 10%
Average
Green
gold