Local detection of infections in heterogeneous networks

In many networks the operator is faced with nodes that report a potentially important phenomenon such as failures, illnesses, and viruses. The operator is faced with the question: Is it spreading over the network, or simply occurring at random? We seek to answer this question from highly noisy and incomplete data, where at a single point in time we are given a possibly very noisy subset of the infected population (including false positives and negatives). While previous work has focused on uniform spreading rates for the infection, heterogeneous graphs with unequal edge weights are more faithful models of reality. Critically, the network structure may not be fully known and modeling epidemic spread on unknown graphs relies on non-homogeneous edge (spreading) weights. Such heterogeneous graphs pose considerable challenges, requiring both algorithmic and analytical development. We develop an algorithm that can distinguish between a spreading phenomenon and a randomly occurring phenomenon while using only local information and not knowing the complete network topology and the weights. Further, we show that this algorithm can succeed even in the presence of noise, false positives and unknown graph edges.