A model of opinion dynamics with echo chambers explains the spatial distribution of vaccine hesitancy

Vaccination hesitancy is a major obstacle to achieving and maintaining herd immunity. It is therefore of prime importance for public health authorities to understand the dynamics of an anti-vaccine opinion in the population. We introduce a novel mathematical model of opinion dynamics with spatial reinforcement, which can generate echo chambers, i.e. opinion bubbles in which information that is incompatible with one's entrenched worldview, is likely disregarded. In a first mathematical part, we scale the model both to a deterministic limit and to a weak-effects limit, and obtain bifurcations, phase transitions, and the invariant measure. In a second part, we fit our model to measles and meningococci vaccination coverage across 413 districts in Germany. We reveal that strong echo chambers explain the occurrence and persistence of the anti-vaccination opinion. We predict and compare the effectiveness of different policies aimed at influencing opinion dynamics in order to increase vaccination uptake.