Random mobility and the spread of infection

We study infection spreading on large static networks when the spread is assisted by a small number of additional virtually mobile agents. For networks which are “spatially constrained”, we show that the spread of infection can be significantly sped up even by a few virtually mobile agents acting randomly. More specifically, for general networks with bounded virulence (e.g., a single or finite number of random virtually mobile agents), we derive upper bounds on the order of the time taken (as a function of network size) for infection to spread. Conversely, for certain common classes of networks such as linear graphs, grids and random geometric graphs, we also derive lower bounds on the order of the spreading time over all (potentially network-state aware and adversarial) virtual mobility strategies. We show that up to a logarithmic factor, these lower bounds for adversarial virtual mobility match the upper bounds on spreading via an agent with random virtual mobility. This demonstrates that random, state-oblivious virtual mobility is in fact order-wise optimal for dissemination in such spatially constrained networks.