A Malware Propagation Model with Dual Delay in the Industrial Control Network

The malware attacks targeting the industrial control network are gradually increasing, and the nonlinear phenomenon makes it difficult to predict the propagation behavior of malware. Once the dynamic system becomes unstable, the propagation of malware will be out of control, which will seriously threaten the security of the industrial control network. So, it is necessary to model and study the propagation of malware in the industrial control network. In this paper, a SIDQR model with dual delay is proposed by fully considering the characteristics of the industrial control network. By analyzing the nonlinear dynamics of the model, the Hopf bifurcation is discussed in detail when the value of dual delay is greater than zero, and the expression for the threshold is also provided. The results of the experiments indicate that the system may have multiple bifurcation points. By comparing different immune and quarantine rates, it is found that the immune rate can be appropriately increased and the isolation rate can be appropriately reduced in the industrial control network, which can suppress the spread of malware without interrupting the industrial production.