  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.
