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Voluntary vaccination is effective to prevent infectious diseases fromspreading. Both vaccination behavior and cognition of the vaccination risk playimportant roles in individual vaccination decision making. However, it is notclear how the co-evolution of the two shapes the population-wide vaccinationbehavior. We establish a coupled dynamics of epidemic, vaccination behavior andperceived vaccination risk with three different time scales. We assume that theincrease of vaccination level inhibits the rise of perceived vaccination risk,and the increase of perceived vaccination risk inhibits the rise of vaccinationlevel. It is shown that the resulting vaccination behavior is similar to thestag-hunt game, provided that the basic reproductive ratio is moderate and thatthe epidemic dynamics evolves fast. This is in contrast with the previous viewthat vaccination is a snowdrift like game. Furthermore, we find that epidemicbreaks out repeatedly and eventually leads to vaccine scares if these threedynamics evolve on a similar time scale. And we propose some ways to promotevaccination behavior, such as controlling side-effect bias and perceivedvaccination costs. Our work sheds light on epidemic control via vaccination bytaking into account the co-evolutionary dynamics of cognition and behavior.

Co-evolution of Vaccination Behavior and Perceived Vaccination Risk can lead to a Stag-Hunt like Game