  In this work, we review the figures used to characterize an epidemic outbreak
most. Particular attention is drawn to epidemic spreading at time-varying
transition rates. A time-varying SIR-like model is used to describe the
epidemic dynamics, from which closed equations relating parameters and key
quantities like reproduction ratio and doubling time are derived. The
definition and computation of these metrics are revisited in the context of the
general solution to the time-varying model dynamics, focusing on the
similarities and differences with the time-invariant case. Further, the
prediction of these metrics, that is of the disease evolution, as response to
different scenarios is also investigated.
