Impact of high-order time-delayed information on epidemic propagation in multiplex networks.

Traditional epidemic models often overlook disease incubation periods and high-order social interactions, limiting their ability to capture real-world transmission dynamics. To address these gaps, we develop a stochastic model that integrates both factors, investigating their combined effects on information diffusion and disease spread. Our framework consists of a two-layer network: an awareness layer, where disease-related information propagates through high-order delayed interactions, and an epidemic layer, where disease transmission follows an SIS model with incubation delays. Using a Markov chain approach, we derive outbreak thresholds and perform numerical simulations to assess the impact of delayed awareness adoption on epidemic outcomes. High-order delayed interactions accelerate information spread compared to traditional pairwise models. Interestingly, while incubation periods increase the risk of hidden transmission, they also provide a crucial window for awareness diffusion, potentially mitigating outbreaks. This dual role of incubation prolonging undetected transmission while enabling proactive awareness dissemination underscores the importance of synchronizing public health interventions with disease incubation phases.