While the interaction between information and diseases in static networks has been extensively investigated, many studies have ignored the characteristics of network evolution. In this study, we construct a new two-layer coupling model to explore the interactions between information and disease. The upper layer describes the diffusion of disease-related information, and the lower layer represents the disease transmission. We then apply power-law distributions to examine the influence of asymmetric activity levels on dynamic propagation, revealing a mapping relationship characterizing the interconnected propagation of information and diseases among partial nodes within the network. Subsequently, we derive the disease outbreak threshold using the microscopic Markov-chain approach (MMCA). Finally, we perform extensive Monte Carlo (MC) numerical simulations to verify the accuracy of our theoretical results. Our findings indicate that the activity levels of individuals in the disease transmission layer have a more significant influence on disease transmission compared with the individual activity levels in the information diffusion layer. Moreover, reducing the damping factor can delay disease outbreaks and suppress disease transmission, while enhancing individual quarantine measures can contribute positively to disease control. This study provides valuable insights for policymakers in developing outbreak prevention and control strategies.