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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.10614 |
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| _version_ | 1866918440967602176 |
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| author | Bondesan, Andrea Borsotti, Jacopo Fontana, Mattia |
| author_facet | Bondesan, Andrea Borsotti, Jacopo Fontana, Mattia |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Kinetic models of opinion-driven epidemic dynamics modulated by graphons Bondesan, Andrea Borsotti, Jacopo Fontana, Mattia Analysis of PDEs Physics and Society Populations and Evolution 35Q84, 82B21, 91D10, 94A17 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. |
| title | Kinetic models of opinion-driven epidemic dynamics modulated by graphons |
| topic | Analysis of PDEs Physics and Society Populations and Evolution 35Q84, 82B21, 91D10, 94A17 |
| url | https://arxiv.org/abs/2604.10614 |