New results on modeling and hybrid control for malware propagation in cyber–physical systems

The structural characteristics of cyber–physical systems (CPSs) make them vulnerable to malware attacks. In order to study the propagation behavior of malware in CPSs, we propose a new malware propagation model, called Susceptible–Infected–Enhanced Infected–Quarantined–Recovered–Susceptible (SI2QRS) model. First, considering the feature that the infectiousness of malware may be enhanced during the propagation process, the SI2QRS model has two different infection rates. And the equilibrium points and the basic reproduction number of the model are derived. Second, the dynamic behavior is analyzed using stability theory and the bifurcation theorem. Given the bifurcation and chaos may arise in systems with time delay, a new hybrid controller is proposed to control the threshold of Hopf bifurcation. Finally, the simulation results show that the controller can bring the model to a stable state by delaying the threshold of Hopf bifurcation, which verifies the validity of the theoretical results.