Simple spatial processes can generate heterogeneous contact distributions in face-to-face interactions
Face-to-face interactions reveal recurring patterns, suggesting the possibility of shared underlying mechanisms. More specifically, inter-contact durations, contact durations and number of contacts per edge share similar heavy-tail distributions in many empirical settings. A common intuition is that face-to-face interactions may be influenced by spatial constraints, and that the observed complex behaviors could arise from such physical limitations. Our models explore the impact of this constraint by simulating pedestrian dynamics, and studying the generated temporal network of contacts. Previous work showed that the inter-contact duration distribution is recovered with a pedestrian dynamic as simple as the two dimensional random walk, but this approach doesn't allow to recover the distribution of the number of times a pair of individuals has been in contact. One assumption is that the number of contact between individual arises from the social relationship between them, in other words a memory of past interactions. However, we here present models that are based on solely spatial rules, by adding simple targeting mechanisms to the two-dimensional random walk. We show that these models allow to recover a broad distribution of the number of contacts, revealing the importance of two ingredients: localized phases and controlled population mixing. This suggests that the observed heterogeneity in the contact numbers within the data does not necessarily emerge from underlying social relationships between individuals, since an equivalent distribution may be reproduced using a purely spatially based model, without the need for memory mechanisms.