A problem in human dynamics: modelling the population density of a social space

Abstract

Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we tackle the problem of determining the distribution of the population density of a social space over time by modelling the dynamics of agents entering and exiting the space as a birth–death process. We show that, for a simple agent-based model in which the probabilities of entering and exiting the space depends on the number of agents currently present in the space, the population density of the space follows a gamma distribution. We also provide empirical evidence supporting the validity of the model by applying it to a data set of occupancy traces of a common space in an office building.

Keywords:

• Human dynamics
• birth–death process
• occupancy density
• social space

Acknowledgements

The authors would like to thank the reviewers for their constructive comments, which have helped us to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Mark Levene http://orcid.org/0000-0001-8632-4732

Trevor Fenner http://orcid.org/0000-0002-4239-7574