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Propagation on networks: an exact alternative perspective
Pierre-André Noël1, Antoine Allard, Laurent Hébert-Dufresne
1Département de Physique, de Génie Physique et d'Optique, Université Laval, Québec (QC), Canada.
Summary
We developed a simple stochastic process to model disease spread on networks. This method simplifies calculations and accurately predicts epidemic behavior, offering computational advantages for various systems.
Area of Science:
- Epidemiology
- Network Science
- Computational Biology
Background:
- Understanding disease dynamics on finite networks is crucial for public health.
- Existing models often struggle with computational complexity on realistic network structures.
Purpose of the Study:
- To develop a computationally efficient and accurate model for susceptible-infectious dynamics on finite networks.
- To simplify analytical calculations for epidemic modeling.
Main Methods:
- Derivation of a birth-death Markov process by generating network structures on-the-fly.
- Utilizing a dual analytical approach: Gaussian approximation for large-scale epidemics and branching process for small outbreaks.
Main Results:
- The derived stochastic process exactly models susceptible-infectious dynamics on finite networks.
- The dual analytical description accurately approximates distributions even for small networks.
- Significant computational advantages and generalization potential were demonstrated.
Conclusions:
- The on-the-fly network generation approach provides a powerful and flexible framework for epidemic modeling.
- This method simplifies complex network dynamics, enabling broader analytical and computational applications in disease spread research.
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