Localized Epidemic Detection in Networks with Overwhelming Noise

We consider the problem of detecting an epidemic in a population where individual diagnoses are extremely noisy. We show that exclusively local, approximate knowledge of the contact network suffices to accurately detect the epidemic. The motivation for this problem is the plethora of examples (influenza strains in humans, or computer viruses in smartphones, etc.) where reliable diagnoses are scarce, but noisy data plentiful. In flu or phone-viruses, exceedingly few infected people/phones are professionally diagnosed (only a small fraction go to a doctor) but less reliable secondary signatures (e.g., people staying home, or greater-than-typical upload activity) are more readily available. Our algorithm requires only local-neighbor knowledge of this graph, and in a broad array of settings that we describe, succeeds even when false negatives and false positives make up an overwhelming majority of the data available. Our results show it succeeds in the presence of partial information about the contact network, and also when are many (hundreds, in our examples) of initial patients-zero.