Tomographic reconstruction of a disease transmission landscape via GPS recorded random paths

Identifying areas in a landscape where individuals have a higher likelihood of disease infection is key to managing diseases. Unlike conventional methods relying on ecological assumptions, we perform a novel epidemiological tomography for the estimation of landscape propensity to disease infection, using GPS animal tracks in a manner analogous to tomographic techniques in positron emission tomography (PET). Treating tracking data as random Radon transforms, we analyze Cervid movements in a game preserve, paired with antibody levels for epizootic hemorrhagic disease virus (EHDV) -- a vector-borne disease transmitted by biting midges. After discretizing the field and building the regression matrix of the time spent by each deer (row) at each point of the lattice (column), we model the binary response (infected or not) as a binomial linear inverse problem where spatial coherence is enforced with a total variation regularization. The smoothness of the reconstructed propensity map is selected by the quantile universal threshold. To address limitations of small sample sizes and evaluate significance of our estimates, we quantify uncertainty using a bootstrap-based data augmentation procedure. Our method outperforms alternative ones when using simulated and real data. This tomographic framework is novel, with no established statistical methods tailored for such data.