Differential Game-Based Strategies for Preventing Malware Propagation in Wireless Sensor Networks

Wireless sensor networks (WSNs) are prone to propagating malware because of special characteristics of sensor nodes. Considering the fact that sensor nodes periodically enter sleep mode to save energy, we develop traditional epidemic theory and construct a malware propagation model consisting of seven states. We formulate differential equations to represent the dynamics between states. We view the decision-making problem between system and malware as an optimal control problem; therefore, we formulate a malware-defense differential game in which the system can dynamically choose its strategies to minimize the overall cost whereas the malware intelligently varies its strategies over time to maximize this cost. We prove the existence of the saddle-point in the game. Further, we attain optimal dynamic strategies for the system and malware, which are bang-bang controls that can be conveniently operated and are suitable for sensor nodes. Experiments identify factors that influence the propagation of malware. We also determine that optimal dynamic strategies can reduce the overall cost to a certain extent and can suppress the malware propagation. These results support a theoretical foundation to limit malware in WSNs.