Optimal quarantining of wireless malware through power control

The topic of malware propagation in mobile wireless networks is gaining momentum among the research community, as actual vulnerabilities are revealed through recent outbreaks of worms. We introduce a defense strategy that quarantines the malware by reducing the communication range. This counter-measure faces us to a trade-off: reducing the communication range suppresses the spread of the malware, however, it also negatively affects the performance of the network as the end-to-end communication delay increases. 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 trade-off 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 two different cost functions.