A game theoretic complex network model to estimate the epidemic threshold under individual vaccination behaviour and adaptive social connections.

In today's interconnected world, the spread of information is closely linked to infectious disease dynamics. Public awareness plays a crucial role, as individual vaccination decisions significantly impact collective efforts to combat emerging health threats. This study explores disease transmission within a framework integrating social connections, information sharing, and individual vaccination decisions. We introduce a behaviour-prevalence model on an adaptive multiplex network, where the physical layer (Layer-II) captures disease transmission under vaccination. In contrast, the virtual layer (Layer-I) represents adaptive social contacts and the flow of information, shaping vaccination decisions within a socially influenced environment. We derive analytical expressions for the epidemic threshold using the microscopic Markov Chain Method (MMCM). Simulation results highlight that adaptive social contacts lead to a higher epidemic threshold than non-adaptive networks. Additionally, network characteristics, such as the power-law exponent in scale-free networks, significantly impact infection spread within populations. Our results reveal that changes in perceived infection risk and an individual's sensitivity to non-vaccinated neighbour's status strongly influence vaccine uptake across populations. These insights can guide public health officials in developing targeted vaccination programs that address the evolving dynamics of social connections, information dissemination, and vaccination choice in the digital era.