Information survival threshold in sensor and P2P networks

Consider a network of, say, sensors, or P2P nodes, or bluetooth-enabled cell-phones, where nodes transmit information to each other and where links and nodes can go up or down. Consider also a 'datum', that is, a piece of information, like a report of an emergency condition in a sensor network, a national traditional song, or a mobile phone virus. How often should nodes transmit the datum to each other, so that the datum can survive (or, in the virus case, under what conditions will the virus die out)? Clearly, the link and node fault probabilities are important - what else is needed to ascertain the survivability of the datum? We propose and solve the problem using non-linear dynamical systems and fixed point stability theorems. We provide a closed-form formula that, surprisingly, depends on only one additional parameter, the largest eigenvalue of the connectivity matrix. We illustrate the accuracy of our analysis on realistic and real settings, like mote sensor networks from Intel and MIT, as well as Gnutella and P2P networks.