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Cluster approximations for epidemic processes: a systematic description of correlations beyond the pair level
Thomas Petermann1, Paolo De Los Rios
1Institut de Physique Théorique, Université de Lausanne, CH-1015, Lausanne, Switzerland. Thomas.Petermann@alumni.ethz.ch
Journal of Theoretical Biology
|June 5, 2004
Summary
This study introduces a new method to accurately model virus spread in structured populations. It improves upon existing approximations by incorporating spatial correlations for better epidemic dynamics prediction.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- Virus spread is a dynamic process on discrete spatial networks.
- Mean-field approximations are inaccurate for lattice-structured populations.
- Existing improvements on pair approximations face challenges in deriving dynamics.
Purpose of the Study:
- To develop a systematic methodology for describing epidemic dynamics in spatially structured populations.
- To account for spatial correlations up to a desired range.
- To provide an improved description of epidemic steady states and invasion dynamics.
Main Methods:
- Representing the population and its connectivity as a homogeneous network.
- Deriving equations for dynamical correlations in a straightforward manner.
- Efficiently solving these equations due to their binary character.
Main Results:
- The proposed method naturally embeds spatial patterns like loops and tree-like structures.
- It offers an improved description of epidemic steady states.
- It enhances the understanding of invasion dynamics in structured populations.
Conclusions:
- The new methodology provides a more accurate framework for modeling epidemic spread in various network topologies.
- It overcomes limitations of traditional mean-field and pair approximations.
- This approach offers a powerful tool for analyzing spatial epidemic dynamics.
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