STSIR: An individual-group game-based model for disclosing virus spread in Social Internet of Things

Social Internet of Things (SIoT) with deep integration of Internet of Things and social networks has become a target of a large number of hackers who attempt to spread viruses for breaching data confidentiality and service reliability. Therefore, exposing the law of virus spread with social characteristics and addressing historical dependence of infection and recovery rates in an SIoT are urgent problems to be solved at present. To this end, we propose a novel virus spread model (STSIR) based on an epidemic theory's analysis framework and individual-group game theory, which more reasonably describes viruses spread among devices considering people behavior. Aiming at the characteristics of SIoTs including limited social distance and dynamic number variation of people and devices, we adopt and improve the traditional epidemic model SIR to reveal the form of viruses continuously spreading to neighbor nodes. We then introduce an individual-group game to establish the attack and defense model between infected SIoT nodes and susceptible SIoT nodes, in order to not only obtain the mixed Nash equilibrium solution by using a payoff matrix but also solve the dependence of the infection and recovery rates on historical experience. Further, we establish differential equations to represent the model STSIR, which are the basis of proving the existence of model equilibrium points and analyzing stability mathematically. Finally, the effectiveness of the model STSIR in curbing virus spread is verified by simulating two equilibrium points. Under the same conditions in an SIoT, the model STSIR reduce viruses by similar to 45% more than the model SIS, and saves stabilization time cost by similar to 66.7% compared with the model SIR, which proves that the model STSIR is obviously more effective.