  Mathematical modeling of disease outbreaks can infer the future trajectory of
an epidemic, which can inform policy decisions. Another task is inferring the
origin of a disease, which is relatively difficult with current mathematical
models. Such frameworks -- across varying levels of complexity -- are typically
sensitive to input data on epidemic parameters, case-counts and mortality
rates, which are generally noisy and incomplete. To alleviate these
limitations, we propose a maximum entropy framework that fits epidemiological
models, provides a calibrated infection origin probabilities, and is robust to
noise due to a prior belief model. Maximum entropy is agnostic to the
parameters or model structure used and allows for flexible use when faced with
sparse data conditions and incomplete knowledge in the dynamical phase of
disease-spread, providing for more reliable modeling at early stages of
outbreaks. We evaluate the performance of our model by predicting future
disease trajectories in synthetic graph networks and the real mobility network
of New York state. In addition, unlike existing approaches, we demonstrate that
the method can be used to infer the origin of the outbreak with accurate
confidence. Indeed, despite the prevalent belief on the feasibility of
contact-tracing being limited to the initial stages of an outbreak, we report
the possibility of reconstructing early disease dynamics, including the
epidemic seed, at advanced stages.
