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A Network Epidemic Model with Preventive Rewiring: Comparative Analysis of the Initial Phase
Tom Britton1, David Juher2, Joan Saldaña3
1Department of Mathematics, Stockholm University, Stockholm, Sweden.
Bulletin of Mathematical Biology
|November 2, 2016
Summary
This study explores epidemic models with preventive rewiring, finding that branching process approximations accurately predict outbreak dynamics and reproduction numbers in random networks, especially when exposed individuals also rewire.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- Stochastic SIR and SEIR models analyze disease spread in populations.
- Random networks are used to model complex social interactions.
- Preventive rewiring introduces adaptive behavior in epidemic models.
Purpose of the Study:
- To analyze early-stage epidemic dynamics in stochastic SIR and SEIR models with preventive rewiring.
- To derive expressions for the basic reproduction number and infectious node degree.
- To compare approximation methods with simulation results on different network types.
Main Methods:
- Development of SIR-[p] and SEIR-[p] models incorporating preventive rewiring.
- Application of branching process and pair approximation techniques.
- Stochastic simulations on Poisson and scale-free networks.
Main Results:
- Both approximation methods yield identical epidemic thresholds and reproduction numbers when only infected nodes rewire.
- Pair approximation overestimates infectious node degree above the epidemic threshold compared to simulations.
- Branching process approximation shows better agreement with simulations, particularly when exposed nodes also rewire.
Conclusions:
- Branching process approximation is a reliable method for predicting epidemic thresholds and reproduction numbers in models with preventive rewiring.
- The accuracy of approximation methods depends on whether exposed individuals engage in rewiring.
- Simulations validate the branching process approximation's effectiveness in capturing early epidemic spread on random networks.
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