The resurgence of measles is largely attributed to the decline in vaccine adoption and the increase in travels . Although the vaccine for measles is readily available and highly successful, its current adoption is not adequate to prevent epidemic . Vaccine adoption is directly affected by vaccination decisions from human behaviour and has a complex interplay with the spatial spread of disease specific to one's travelling network. In this paper, we focus on modelling the travelling network as scale-free network to investigate the correlation between the network's assortativity and the resultant epidemic and vaccination dynamics , by adopting a SIR-network model in game-theoretic framework with imitation dynamics under  voluntary vaccination scheme. Our results show a non-linear correlation between epidemic dynamics and  network's assortativity, highlighting that highly disassortative networks are particularly impactful at containing epidemics . To explain the finding, we propose a novel network-theoretic measure, \psi, defined as the ratio between Shannon information and maximum coreness. Higher \psi is found in highly disassortative networks, which provides an explanation on why disassortative networks may be better at suppressing epidemics. Furthermore, We find that \psi has a monotonically decreasing relationship with cumulative incidence, indicating that higher \psi corresponds to lower cumulative incidence .
The resurgence of measles is largely attributed to the decline in vaccine adoption and the increase in mobility . Although the vaccine for measles is readily available and highly successful, its current adoption is not adequate to prevent epidemics . Vaccine adoption is directly affected by individual vaccination decisions, and has a complex interplay with the spatial spread of disease shaped by an underlying mobility (travelling) network. In this paper, we model the travelling connectivity as a scale-free network , and investigate dependencies between the network's assortativity and the resultant epidemic and vaccination dynamics . In doing so we extend an SIR-network model with game-theoretic components, capturing the imitation dynamics under a voluntary vaccination scheme. Our results show a correlation between the epidemic dynamics and the network's assortativity, highlighting that networks with high assortativity tend to suppress epidemics under certain conditions. In highly assortative networks, the suppression is sustained producing an early convergence to equilibrium. In highly disassortative networks, however, the suppression effect diminishes over time due to scattering of non-vaccinating nodes, and frequent switching between the predominantly vaccinating and non-vaccinating phases of the dynamics .
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highly disassortative networks are particularly impactful at containing epidemics . To explain the finding, we propose a novel network-theoretic measure, \psi, defined as the ratio between Shannon information and maximum coreness. Higher \psi is found in
networks with high assortativity tend to suppress epidemics under certain conditions. In highly assortative networks, the suppression is sustained producing an early convergence to equilibrium. In
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which provides an explanation on why disassortative networks may be better at suppressing epidemics. Furthermore, We find that \psi has a monotonically decreasing relationship with cumulative incidence, indicating that higher \psi corresponds to lower cumulative incidence
however, the suppression effect diminishes over time due to scattering of non-vaccinating nodes, and frequent switching between the predominantly vaccinating and non-vaccinating phases of the dynamics