Kinetic models of opinion-driven epidemic dynamics modulated by graphons
Andrea Bondesan, Jacopo Borsotti, Mattia Fontana
TLDR
This paper introduces kinetic models to simulate opinion-driven epidemic dynamics on social networks represented by graphons, showing how opinions and leaders affect disease spread.
Key contributions
- Introduces kinetic models for opinion-driven epidemic dynamics on graphon-based social networks.
- Proves model convergence to equilibrium using $L^1$ norm and Sobolev space techniques.
- Develops a structure-preserving scheme showing opinion leaders limit spread, but influenceable individuals worsen epidemics.
- Identifies a novel time-dependent quantity that can generate epidemic waves without external forcing.
Why it matters
This research offers a novel framework to understand the complex interplay between social opinions and epidemic spread. It highlights how opinion leaders and individual susceptibility critically influence disease control, showing social factors can intrinsically drive epidemic waves.
Original Abstract
We introduce kinetic models to simulate epidemic spread while accounting for individuals' opinions on protective behaviors. Opinion exchanges occur on a social network represented by a graphon, leading to scenarios with or without opinion leaders. We prove convergence to equilibrium in the strong $L^1$ norm via relative entropy methods and in homogeneous Sobolev spaces $\dot{H}^{-s}$, $s \in \big(\frac{1}{2},1\big)$, using Fourier-based techniques. We then design a structure-preserving scheme for the coupled opinion-epidemiological system, highlighting graphon effects: opinion leaders supporting protective behaviors limit disease spread, whereas influenceable individuals may shift toward opposing views, worsening epidemics. Finally, we introduce a time-dependent quantity, analogous to the reproduction number, whose oscillations can generate epidemic waves without explicit external forcing. The MATLAB code implementing our algorithms is made publicly available.
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