An infection is spreading through a city, and residents are watching each other: some have already been vaccinated, others are hesitant. Every day, they update their decisions — whether to imitate neighbors or friends who support vaccination.
The key finding: if connections between people form not just pairs but triples (a hypergraph), then even without strong pressure, pockets of vaccinated individuals emerge. These pockets act like fences, stopping the wave of disease. But when support from friends becomes too pushy, people stop changing their minds, and the unvaccinated accumulate again.
The optimum is moderate pressure — about half of the maximum. Then vaccination coverage is highest, and outbreaks are suppressed. It's like getting advice from friends: a gentle nudge helps, but nagging turns people off.
The model used a square lattice, like a chessboard where each cell is a person, and contacts are only with neighbors to the sides.