Dynamic and thermodynamic origins of non-equilibrium phase transitions in infectious disease networks.

Understanding the mechanisms driving phase transitions in epidemic dynamics is essential for predicting and controlling infectious disease outbreaks. In this study, we apply the landscape and flux framework from nonequilibrium statistical physics to investigate the physical origins of bifurcations, or nonequilibrium phase transitions, in adaptive epidemic networks. Using a SIRS model, we systematically examine how variations in the rewiring rate (representing individuals' behavioral responses to avoid infection) and the average node degree (indicating the population's contact density) reshape the topography of the system's potential landscape and alter barrier heights, thereby triggering transitions between bistable and monostable regimes. Our findings reveal that rotational flux acts as a nonequilibrium driving force underlying these transitions, while the entropy production rate quantifies the associated thermodynamic cost. In addition, we identify critical slowing down, time irreversibility, and flickering frequency as effective early warning indicators of critical transitions when the rewiring rate or the average node degree of the network changes. These results offer quantitative tools and potential strategies for anticipating abrupt public health crises.