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.
as written by the authors arXiv:2601.12114
Vaccination games in higher-order settings remain underexplored, despite their importance in shaping opinions and collective decisions. Here, we introduce a parsimonious behavioral-epidemiological model to evaluate how peer reinforcement pressure influences vaccination uptake. The framework consists of a two-layer multiplex: an epidemic layer governed by the SIR process on a square lattice, and a behavioral layer represented by a hypergraph of triadic interactions. Individuals update their vaccination strategy via imitation, modulated by a reinforcement parameter $$\alpha$$ when peer support is present. We find that higher-order structure alone induces clusters of vaccinated individuals that act as protective barriers. Low but nonzero reinforcement ($$\alpha \approx 0.5$$) maximizes coverage and suppresses outbreaks, while both negligible ($$\alpha \approx 0$$) and moderate ($$\alpha > 0.1$$) reinforcement reduce uptake, as excessive confirmation lowers adaptability and enables non-vaccinators to re-emerge. Our work bridges complex contagion theory with evolutionary game dynamics, offering insights into how contact structure and peer reinforcement jointly shape vaccination behavior.
The model used a square lattice, like a chessboard where each cell is a person, and contacts are only with neighbors to the sides.