Propagation Dynamics of Network System in Response to the Resource-Consuming Attack

Modeling and analysis play a crucial role in the prevention, safeguarding, and assessment of network security. However, existing literature on network security modeling overlooks the realistic convertibility between malware states. Thus, based on the susceptible–infected–susceptible compartmental model, this study proposes a susceptible–infected–exhausted–susceptible model that includes an enhanced transition pathway of the malware state. Subsequently, considering the potential heterogeneity of network topology and pulse wave attacks (PA), three additional models are expanded upon. Concurrently, the dynamic stability analyses of these four models have been conducted to verify the practicality of effective control by malicious attackers (MA) and network defenders (ND) within these frameworks to achieve their respective benefits. Finally, based on the framework of optimal control and game theory, we discuss and simulate attack–defense confrontation under various scenarios, including different objective functions, network topologies, control forms, and parameter combinations. Experimental results demonstrate that in most cases, MA refrained from launching malicious attacks but continued malware propagation. Under certain conditions, malware may remain in a dormant state indefinitely. Meanwhile, ND consistently engages in network repair regardless of MA's actions. MA's revenue peaks when launching continuous-time attacks in the financial network, while ND's revenue is at its lowest. In the majority of instances, under PA and higher operation costs, MA's efficacy is lower, while ND performs better.