Kinetic models of opinion-driven epidemic dynamics modulated by graphons

TL;DR

This paper develops kinetic models for epidemic spread influenced by social opinions on a graphon, analyzing equilibrium convergence, designing structure-preserving schemes, and exploring opinion effects on epidemic waves, with MATLAB code available.

Contribution

It introduces a novel kinetic modeling framework incorporating opinion dynamics on graphons, with convergence proofs, numerical schemes, and analysis of opinion influence on epidemic outcomes.

Findings

Opinion leaders support protective behaviors and reduce disease spread.

Influenceable individuals may oppose protective measures, worsening epidemics.

Oscillations in a reproduction number-like quantity can generate epidemic waves.

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.