Background Theoretical studies predict that it is not possible to eradicate a disease under voluntary vacci- nation because of the emergence of non-vaccinating “free-riders” when vaccination coverage increases. A central tenet of this approach is that human behaviour follows an economic model of rational choice. Yet,empirical studies reveal that vaccination decisions do not nec- essarilymaximize individual self-interest. Here we investigate the dynamics of vaccination coverage using an approach that dispenses with payoff maximization and assumes that risk perception results fromthe interaction between epidemiology and cognitive biases. Methods We consider a behaviour-incidencemodel in which individuals perceive actual epidemiological risks as a function of their opinion of vaccination. As a result of confirmation bias, sceptical indi- viduals (negative opinion) overestimate infection costwhile pro-vaccines individuals (positive opinion) overestimate vaccination cost.Weconsidered a feedback between individuals and their environment as individuals could change their opinion, and thus theway they perceive risks, as a function of both the epidemiology and themost common opinion in the population. Results For all parameter values investigated, the infection is never eradicated under voluntary vac- cination. For moderately contagious diseases, oscillations in vaccination coverage emerge because individuals process epidemiological information differently depending on their opinion. Conformismdoes not generate oscillations but slows down the cultural response to epidemiological change. Conclusion Failure to eradicate vaccine preventable disease emerges from the model because of cog- nitive biases that maintain heterogeneity in how people perceive risks. Thus, assumptions of economic rationality and payoff maximization are not mandatory for predicting commonly observed dynamics of vaccination coverage. This model shows that alternative notions of rationality, such as that of ecological rationality whereby individuals use simple cognitive heuristics, offer promising new avenues for modelling vaccination behaviour.