Pinning control of an epidemic network model with time-varying weights

This work develops a two-layer coupled network model with key structural features. The epidemic layer is bidirectional with time-varying contact weights, while the information layer is directed with normalized influence weights. Using the Microscopic Markov Chain Approximation framework, we derive the epidemic transmission threshold and confirm its accuracy through Monte Carlo simulations. Building on these findings, we design a degree-based pinning control is designed on the information layer. The optimal fixed node degree is further determined to minimize the comprehensive cost of the cure burden and intervention efforts while enhancing epidemic suppression through self-protection. The strong consistency between theoretical analysis and simulation results verifies the effectiveness of the model, indicating that pinning control is an effective and practical strategy for epidemic prevention and control in complex networks.