A Mathematical Model of Opinion Dynamics with Application to Vaccine Denial
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908677484576768 |
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| author | Cicala, Daniel Jiang, Yi Lee, Jane HyoJin Kurianski, Kristin Ledder, Glenn |
| author_facet | Cicala, Daniel Jiang, Yi Lee, Jane HyoJin Kurianski, Kristin Ledder, Glenn |
| contents | Public health outcomes can be heavily influenced by the landscape of public opinion; hence, it is important to understand how that landscape changes over time. For one, opinions on public health issues are responsive to official pronouncements, whether from the governmental or professional medical establishments. Additionally, in today's world of high speed communication, opinion can also be highly responsive to the broadcast opinions of "influencers" whose large numbers of followers assure them of a broad reach. To understand the opinion landscape in a general sense, we develop an ordinary differential equation model for opinion change that is based primarily on attraction to the opinions of prominent sources. The individual opinion change model is then used to develop a Fokker-Planck-type partial differential equation model for the overall opinion landscape. This model is shown to have a stable equilibrium solution, and the dependence of the equilibrium solution on key model parameters is illustrated with examples based on opinion regarding vaccination. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_18166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Mathematical Model of Opinion Dynamics with Application to Vaccine Denial Cicala, Daniel Jiang, Yi Lee, Jane HyoJin Kurianski, Kristin Ledder, Glenn Physics and Society Dynamical Systems 35Q91 (Primary), 91D30, 35B35, 35Q84, 35K20 Public health outcomes can be heavily influenced by the landscape of public opinion; hence, it is important to understand how that landscape changes over time. For one, opinions on public health issues are responsive to official pronouncements, whether from the governmental or professional medical establishments. Additionally, in today's world of high speed communication, opinion can also be highly responsive to the broadcast opinions of "influencers" whose large numbers of followers assure them of a broad reach. To understand the opinion landscape in a general sense, we develop an ordinary differential equation model for opinion change that is based primarily on attraction to the opinions of prominent sources. The individual opinion change model is then used to develop a Fokker-Planck-type partial differential equation model for the overall opinion landscape. This model is shown to have a stable equilibrium solution, and the dependence of the equilibrium solution on key model parameters is illustrated with examples based on opinion regarding vaccination. |
| title | A Mathematical Model of Opinion Dynamics with Application to Vaccine Denial |
| topic | Physics and Society Dynamical Systems 35Q91 (Primary), 91D30, 35B35, 35Q84, 35K20 |
| url | https://arxiv.org/abs/2511.18166 |