  The interplay of biological, social, structural and random factors makes
disease forecasting extraordinarily complex. The course of an epidemic exhibits
average growth dynamics determined by features of the pathogen and the
population, yet also features significant variability reflecting the stochastic
nature of disease spread. In this work, we reframe a stochastic branching
process analysis in terms of probability generating functions and compare it to
continuous time epidemic simulations on networks. In doing so, we predict the
diversity of emerging epidemic courses on both homogeneous and heterogeneous
networks. We show how the challenge of inferring the early course of an
epidemic falls on the randomness of disease spread more so than on the
heterogeneity of contact patterns. We provide an analysis which helps quantify,
in real time, the probability that an epidemic goes supercritical or
conversely, dies stochastically. These probabilities are often assumed to be
one and zero, respectively, if the basic reproduction number, or R0, is greater
than 1, ignoring the heterogeneity and randomness inherent to disease spread.
This framework can give more insight into early epidemic spread by weighting
standard deterministic models with likelihood to inform pandemic preparedness
with probabilistic forecasts.
