Estimating Spread of Contact-Based Contagions in a Population Through Sub-Sampling

Various phenomena such as viruses, gossips, and physical objects (e.g., packages and marketing pamphlets) can be spread through physical contacts. The spread depends on how people move, i.e., their mobility patterns. In practice, mobility patterns of an entire population is never available, and we usually have access to location data of a subset of individuals. In this paper, we formalize and study the problem of estimating the spread of a phenomena in a population, given that we only have access to sub-samples of location visits of some individuals in the population. We show that simple solutions that estimate the spread in the sub-sample and scale it to the population, or more sophisticated solutions that rely on modeling location visits of individuals do not perform well in practice. Instead, we directly model the co-locations between the individuals. We introduce PollSpreader and PollSusceptible, two novel approaches that model the co-locations between individuals using a contact network, and infer the properties of the contact network using the sub-sample to estimate the spread of the phenomena in the entire population. We analytically show that our estimates provide an upper bound and a lower bound on the spread of the disease in expectation. Finally, using a large high-resolution real-world mobility dataset, we experimentally show that our estimates are accurate in practice, while other methods that do not correctly account for co-locations between individuals result in entirely wrong observations (e.g, premature prediction of herd-immunity).