A Mathematical Model of Opinion Dynamics with Application to Vaccine Denial

TL;DR

This paper develops a mathematical model using differential equations to understand how public opinions, especially about vaccination, evolve over time influenced by authorities and influencers, revealing stable opinion states.

Contribution

It introduces a novel differential equation framework for modeling opinion dynamics influenced by prominent sources, applicable to public health issues like vaccination.

Findings

The model exhibits a stable equilibrium of opinions.

Equilibrium depends on key parameters such as influence strength.

Application to vaccination opinions demonstrates the model's relevance.

Abstract

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.