Understanding individuals' voluntary vaccinating behaviors plays essential roles in making vaccination policies for many vaccinepreventable diseases. Usually, individuals decide whether to vaccinate through evaluating the relative cost of vaccination and infection according to their own interests. Mounting evidence shows that the best vaccine coverage level for the population as a whole can hardly be achieved due to the effects of herd immunity. In this paper, taking into consideration the herd immunity threshold, we present an evolutionary N-person threshold game, where individuals can dynamically adjust their vaccinating strategies and their payoffs depend nonlinearly on whether or not the herd immunity threshold is reached. First, in well-mixed populations, we analyze the relationships at equilibrium among the fraction of vaccinated individuals, the population size, the basic reproduction number and the relative cost of vaccination and infection. Then, we carry out simulations on four types of complex networks to explore the evolutionary dynamics of the N-person threshold game in structured populations. Specifically, we investigate the effects of disease severity and population structure on the vaccine coverage for different relative costs of vaccination and infection. The results and findings can offer new insight into designing incentive-based vaccination policies for disease intervention and control.
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