Optimal treatment allocations in space and time for on-line control of an emerging infectious disease

A key component in controlling the spread of an epidemic is deciding where, when and to whom to apply an intervention. We develop a framework for using data to inform these decisions in realtime. We formalize a treatment allocation strategy as a sequence of functions, one per treatment period, that map up-to-date information on the spread of an infectious disease to a subset of locations where treatment should be allocated. An optimal allocation strategy optimizes some cumulative outcome, e.g. the number of uninfected locations, the geographic footprint of the disease or the cost of the epidemic. Estimation of an optimal allocation strategy for an emerging infectious disease is challenging because spatial proximity induces interference between locations, the number of possible allocations is exponential in the number of locations, and because disease dynamics and intervention effectiveness are unknown at out-break. We derive a Bayesian on-line estimator of the optimal allocation strategy that combines simulation-optimization with Thompson sampling. The estimator proposed performs favourably in simulation experiments. This work is motivated by and illustrated using data on the spread of white nose syndrome, which is a highly fatal infectious disease devastating bat populations in North America.