Abstract:

Previous game theoretical analyses of vaccinating behaviour have underscored the strategic interaction between individuals attempting to maximize their health states, in situations where an individual's health state depends upon the vaccination decisions of others due to the presence of herd immunity. Here, we extend such analyses by applying the theories of variational inequalities (VI) and projected dynamical systems (PDS) to vaccination games. These techniques provide a dynamics which give the conditions for existence, uniqueness and stability properties of Nash equilibria. Here they are used to analyze the dynamics of vaccinating behaviour in a population consisting of distinct social groups, where each group has different perceptions of vaccine and disease risks. We find that a population with a majority group and a vaccine-averse minority group usually exhibits higher vaccine coverage than the corresponding homogeneous population, unless the vaccine is perceived to carry very low risk relative to the disease. Moreover, we find that minority groups will tend to exhibit more extreme changes in vaccination behaviour for a given change in risk perception, in comparison to majority groups. These results emphasize the important role played by social heterogeneity in vaccination behaviour, while also highlighting the valuable role that can be played by PDS and VI in mathematical epidemiology.