Optimal Quarantining of Wireless Malware Through Reception Gain Control

Containment of worms constitutes an important challenge in mobile wireless networks as recent outbreaks have revealed actual vulnerabilities. We introduce a defense strategy that quarantines the malware by reducing the communication range. This countermeasure confronts us with a tradeoff: reducing the communication range suppresses the spread of the malware; however, it also deteriorates the network performance. We model the propagation of the malware as a deterministic epidemic. Using an optimal control framework, we select the optimal communication range that captures the above tradeoff by minimizing a global cost function. Using Pontryagin's Maximum Principle, we derive structural characteristics of the optimal communication range as a function of time for general cost functions. Our numerical computations reveal that the dynamic optimal control of the communication range significantly outperforms static choices and is also robust to errors in estimation of the network and attack parameters.