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Continuous-time process for human contact dynamics.

Robin Persoons¹, Matteo D'Alessandro¹, Piet Van Mieghem¹

¹Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, The Netherlands.

Physical Review. E

|October 21, 2025

Summary

This summary is machine-generated.

We introduce a continuous-time Markov model for human contact dynamics, the continuous random walkers induced temporal graph model (CRWIG). This model captures complex human mobility patterns, including arbitrary flight and pause times, with a non-Markovian extension.

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Area of Science:

Complex Systems
Network Science
Stochastic Processes

Background:

Human contact dynamics are crucial for understanding disease spread and social interactions.
Existing models often simplify mobility patterns, limiting their real-world applicability.

Purpose of the Study:

To develop a novel continuous-time Markov model for human contact dynamics.
To analyze the emergent properties of walker interactions and contact graph formation.
To extend the model for non-Markovian behaviors and compare with empirical human mobility data.

Main Methods:

Development of the continuous random walkers induced temporal graph (CRWIG) model.
Mathematical formulation of the Markov governing equation for walker ensemble.
Analysis of time discretization effects and proof of exponential decay and intermeeting time tails.
Extension to a non-Markovian model with non-exponential sojourn times.

Main Results:

CRWIG exhibits exponential decay of initial conditions and exponentially tailed intermeeting times.
The non-Markovian extension accurately reproduces empirical human mobility: arbitrary flight/pause distributions.
The extended model yields power-law intermeeting time distributions with exponential tails.

Conclusions:

The CRWIG model provides a robust framework for studying human contact dynamics.
The non-Markovian extension significantly enhances the model's ability to capture real-world human mobility.
This work offers valuable insights for fields like epidemiology, urban planning, and social network analysis.