Co-evolution dynamics between information and epidemic with asymmetric activity levels and community structure in time-varying multiplex networks

During an epidemic outbreak, apart from individual behavior and internal factors, certain external elements typically exert a significant influence on the propagation process. This paper introduces an innovative two-layer model, denoted "unaware–aware–unaware–susceptible–infected–susceptible" (UAU-SIS) model, encompassing two dynamic processes in time-varying multiplex networks. The model considers the effects of asymmetric individual activity levels and distinct network topologies on the dynamic propagation process. Importantly, we also explore how global and local environmental stresses impact individual behavior changes. To quantify the influence of individual behavior changes on dynamic propagation, we employ the Heaviside step function. We also employ a power-law distribution to describe varying individual activity levels for each layer to characterize the influence of asymmetric individual activity levels on epidemic transmission. Using the microscopic Markov chain approach (MMCA), we establish the probabilistic transfer equation for each state and derive the epidemic outbreak threshold. Comprehensive Monte Carlo (MC) simulations were performed to validate our theoretical findings, with the results demonstrating that reducing community mobility and decreasing the threshold for behavior change can effectively delay outbreaks and limit the scale of an epidemic. The sensitivity of local environmental stresses is more capable of influencing individual behavioral decision-making. Furthermore, activity levels in the physical contact network exert a greater impact on epidemic transmission compared to those in the information diffusion layer. Notably, varying individual thresholds for behavior change result in a two-phase effect on both the epidemic outbreak threshold and its ultimate scale. Hence, this study provides actionable insights for policymakers responsible for shaping vaccination strategies and managing epidemic transmission.