Impact of imperfect vaccination and defense against contagion on vaccination behavior in complex networks

We explore a mathematical framework of the vaccination game taking into account spatial structure, say, and degree distribution amid individuals. The framework presumes SIR/V dynamics in a season, which is followed by a strategy update process that estimates whether an individual will take a protecting measure, considering imperfect vaccination or defense against contagion. The numerical result based on multi-agent simulations (MAS) validates our theory, suggesting that a more heterogeneous spatial structure is vulnerable to an epidemic. This conclusion is consistent with the qualitative knowledge that a pandemic arises more easily in a scale-free network than in homogeneous networks because of the negative contribution of hub agents acting as super spreaders. Highlights - A new theoretical model is established for the vaccination game with a SIR/V model and either imperfect vaccination or intermediate measures. - The model considers degree distribution amid individuals, which significantly influences disease spreading. - The model is validated by simulation results. - The results prove that a more heterogeneous network is disadvantageous to prevent disease spreading.