SIHQR model with time delay for worm spread analysis in IIoT-enabled PLC network

Abstract

Industrial Internet of Things (IIoT) is a product of deep integration between Internet of Things (IoT) and industrial control networks. As an important component of IIoT, Programmable Logic Controller (PLC) has become a springboard for many hackers to disrupt industrial networks by spreading viruses. It is known that worm can cause enormous loss. Therefore, revealing the rules of worm spread in PLC networks and exploring methods to inhibit worm spread are increasingly important. To this end, we propose a new worm spread model named SIHQR with time delay. Additionally, we establish a game model between susceptible and infected nodes in order to express the infection rate by several game parameters. Through analysis, we discuss the conditions for the emergence of three scenarios: disease-free equilibrium, endemic equilibrium and Hopf bifurcation. We study the stability at the equilibrium points and obtain an expression for a threshold value which determines whether the system exhibits endemic equilibrium or Hopf bifurcation. In the experimental section, we analyze the impact of initial values of node states and the magnitude of game parameters on worm spread in the three aforementioned scenarios. Finally, we propose a method to mitigate or even eliminate the Hopf bifurcation. The experimental results show that the proposed model has welldone performance.