Epidemic Spreading with External Agents

TL;DR

This paper investigates how external agents can accelerate epidemic spreading in large networks, providing bounds and demonstrating the effectiveness of simple random strategies in spatially constrained networks.

Contribution

It introduces bounds on spreading times with external agents and shows the near-optimality of random spreading policies in certain network classes.

Findings

External agents can significantly speed up epidemic spread in spatial networks.

Random spreading policies are order-wise optimal in line graphs, grids, and geometric graphs.

Abstract

We study epidemic spreading processes in large networks, when the spread is assisted by a small number of external agents: infection sources with bounded spreading power, but whose movement is unrestricted vis-\`a-vis the underlying network topology. For networks which are `spatially constrained', we show that the spread of infection can be significantly speeded up even by a few such external agents infecting randomly. Moreover, for general networks, we derive upper-bounds on the order of the spreading time achieved by certain simple (random/greedy) external-spreading policies. Conversely, for certain common classes of networks such as line 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) external-spreading policies; these adversarial lower bounds match (up to logarithmic factors) the spreading time achieved by an external agent with a random spreading policy. This demonstrates that random, state-oblivious infection-spreading by an external agent is in fact order-wise optimal for spreading in such spatially constrained networks.