  We consider the problem of detecting an epidemic in a population where
individual diagnoses are extremely noisy. 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/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. These
secondary data are often plagued by unreliability: many people with the flu do
not stay home, and many people that stay home do not have the flu. This paper
identifies the precise regime where knowledge of the contact network enables
finding the needle in the haystack: we provide a distributed, efficient and
robust algorithm that can correctly identify the existence of a spreading
epidemic from highly unreliable local data. 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 fraction of the data available. Our results show it succeeds in
the presence of partial information about the contact network, and also when
there is not a single "patient zero", but rather many (hundreds, in our
examples) of initial patient-zeroes, spread across the graph.
