  Predictability of undesired events is a question of great interest in many
scientific disciplines including seismology, economy, and epidemiology. Here,
we focus on the predictability of invasion of a broad class of epidemics caused
by diseases that lead to permanent immunity of infected hosts after recovery or
death. We approach the problem from the perspective of the science of
complexity by proposing and testing several strategies for the estimation of
important characteristics of epidemics, such as the probability of invasion.
Our results suggest that parsimonious approximate methodologies may lead to the
most reliable and robust predictions. The proposed methodologies are first
applied to analysis of experimentally observed epidemics: invasion of the
fungal plant pathogen \emph{Rhizoctonia solani} in replicated host microcosms.
We then consider numerical experiments of the SIR
(susceptible-infected-removed) model to investigate the performance of the
proposed methods in further detail. The suggested framework can be used as a
valuable tool for quick assessment of epidemic threat at the stage when
epidemics only start developing. Moreover, our work amplifies the significance
of the small-scale and finite-time microcosm realizations of epidemics
revealing their predictive power.
