Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics

Sabrina Bonandin; Mattia Zanella; Sabrina Bonandin; Mattia Zanella

doi:10.3934/nhm.2024011

Networks and Heterogeneous Media

2024, Volume 19, Issue 1: 235-261. doi: 10.3934/nhm.2024011

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Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics

Sabrina Bonandin ¹,
Mattia Zanella ^{2
,
,}

1.
Institute of Applied Mathematics (IGPM), RWTH Aachen University, Templergraben 55, 52066 Aachen, Germany
2.
Department of Mathematics "F. Casorati", University of Pavia, Via Ferrata 5, 27100 Pavia, Italy

Received: 14 November 2023 Revised: 02 February 2024 Accepted: 18 February 2024 Published: 27 February 2024

In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of kinetic equations for the evolution of the opinion density in each compartment. In the quasi-invariant limit we may show positivity and uniqueness of the solution of the problem together with its convergence towards an equilibrium distribution exhibiting bimodal shape. The tendency of the system towards opinion clusters is further analyzed by means of numerical methods, which confirm the consistency of the kinetic model with its moment system whose evolution is approximated in several regimes of parameters.
- kinetic equations,
- mathematical epidemiology,
- opinion dynamics,
- collective phenomena,
- many-agent systems
Citation: Sabrina Bonandin, Mattia Zanella. Effects of heterogeneous opinion interactions in many-agent systems for epidemic dynamics[J]. Networks and Heterogeneous Media, 2024, 19(1): 235-261. doi: 10.3934/nhm.2024011

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Abstract

In this work we define a kinetic model for understanding the impact of heterogeneous opinion formation dynamics on epidemics. The considered many-agent system is characterized by nonsymmetric interactions which define a coupled system of kinetic equations for the evolution of the opinion density in each compartment. In the quasi-invariant limit we may show positivity and uniqueness of the solution of the problem together with its convergence towards an equilibrium distribution exhibiting bimodal shape. The tendency of the system towards opinion clusters is further analyzed by means of numerical methods, which confirm the consistency of the kinetic model with its moment system whose evolution is approximated in several regimes of parameters.

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