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Pairwise approximation for SIR-type network epidemics with non-Markovian recovery
1Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged 6720, Hungary.
Proceedings. Mathematical, Physical, and Engineering Sciences
|March 7, 2018
Summary
We developed generalized models for non-Markovian epidemics, allowing for varied recovery times. These models accurately approximate epidemic spread over time on networks.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- Non-Markovian epidemic models are crucial for understanding disease dynamics with complex recovery patterns.
- Existing models often simplify recovery time distributions, limiting their applicability.
- Network structure significantly influences epidemic transmission and outcomes.
Purpose of the Study:
- To present generalized mean-field and pairwise models for non-Markovian epidemics on networks.
- To incorporate arbitrary recovery time distributions into epidemic modeling.
- To provide a framework for approximating the time evolution and final size of epidemics.
Main Methods:
- Formulation of a hyperbolic partial differential equation (PDE) system structured by age since infection.
- Reduction of the PDE system to integro-differential equations for analytical and numerical analysis.
- Derivation of new pairwise models for gamma- and uniformly distributed infectious periods.
- Validation through comparison with stochastic network simulations.
Main Results:
- An implicit analytical expression for the final epidemic size and pairwise reproduction number was derived.
- The generalized pairwise model effectively approximates the time evolution of epidemics.
- New models were developed for specific non-exponential recovery time distributions.
- Theoretical findings were confirmed by simulation results.
Conclusions:
- The generalized mean-field and pairwise models offer a flexible framework for non-Markovian epidemics with arbitrary recovery times.
- These models provide accurate approximations for epidemic dynamics on networks.
- The developed models extend the applicability of mathematical epidemiology to more realistic scenarios.
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