Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10614 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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.