Modeling and Analysis in the Industrial Internet with Dual Delay and Nonlinear Infection Rate

This study proposes a novel virus propagation model designed explicitly for SCADA(supervisory Control and Data Acquisition) industrial networks. It addresses a critical limitation in existing models applied to the Internet and Industrial Internet of Things (IIoT)—their failure to account for inter-node information exchange processes. The model is inspired by the phenomenon that “immune” nodes in real-world and biological systems inhibit the spread of viruses by exchanging information. This model incorporates isolation strategies to curb virus transmission, considering the uncertainty of vulnerable device behavior. Central to this research are the assumptions of a nonlinear infection rate and dual delays, which better mirror the real-world conditions of industrial control networks. This approach diverges significantly from prior studies that relied on bilinear infection rate assumptions. This study constructed an SMIQR model through theoretical derivation and experimental validation. The model enables nodes to autonomously enhance their defenses after receiving risk information while accounting for the impact of inter-node information exchange. Experiments based on real-world data demonstrated the model’s effectiveness in simulating virus propagation and evaluating defense strategies, overcoming the limitations of traditional bilinear infection rate assumptions. Comparative experiments show that the SMIQR model significantly reduces the number of infected nodes in SCADA industrial networks, demonstrating its superior effectiveness in curbing virus spread. Furthermore, the research proposed dynamic isolation tactics that balance industrial operational continuity, providing SCADA industrial networks with a theoretical framework (incorporating nonlinear infection rates and dual delay characteristics) and practical defense solutions to curb malware spread without disrupting production.