Echo chambers and opinion dynamics explain the occurrence of vaccination hesitancy.

Vaccination hesitancy is a major obstacle to achieving and maintaining herd immunity. Therefore, public health authorities need to understand the dynamics of an anti-vaccine opinion in the population. We introduce a spatially structured mathematical model of opinion dynamics with reinforcement. The model allows as an emergent property for the occurrence of echo chambers, i.e. opinion bubbles in which information that is incompatible with one's entrenched worldview, is probably disregarded. We scale the model both to a deterministic limit and to a weak-effects limit, and obtain bifurcations, phase transitions and the invariant measure. Fitting the model to measles and meningococci vaccination coverage across Germany, reveals that the emergence of echo chambers dynamics explains the occurrence and persistence of the anti-vaccination opinion in allowing anti-vaxxers to isolate and to ignore pro-vaccination facts. We predict and compare the effectiveness of different policies aimed at influencing opinion dynamics in order to increase vaccination uptake. According to our model, measures aiming at reducing the salience of partisan anti-vaccine information sources would have the largest effect on enhancing vaccination uptake. By contrast, measures aiming at reducing the reinforcement of vaccination deniers are predicted to have the smallest impact.