Abstract
We propose an age-structured model based on game theory to investigate the dynamics of imitation in vaccination decisions. In our model, the rate at which individuals switch vaccination strategies is proportional to the perceived payoffs and media information. We analyze the existence and local stability of equilibria and demonstrate the possibility of Hopf bifurcation. Additionally, we establish the global stability of boundary equilibria and the persistence of the disease. The theoretical results are supported by numerical simulations. This model can be applied to study vaccination behavior among individuals of different ages and infectious disease stages, providing insights for the formulation of effective public health policies.
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