The initial transient phase of an emerging epidemic is of critical importance
for data-driven model building, model-based prediction of the epidemic trend,
and articulation of control/prevention strategies. In principle, quantitative
models for real-world epidemics need to be memory-dependent or non-Markovian,
but this presents difficulties for data collection, parameter estimation,
computation and analyses. In contrast, the difficulties do not arise in the
traditional Markovian models. To uncover the conditions under which Markovian
and non-Markovian models are equivalent for transient epidemic dynamics is
outstanding and of significant current interest. We develop a comprehensive
computational and analytic framework to establish that the transient-state
equivalence holds when the average generation time matches and average removal
time, resulting in minimal Markovian estimation errors in the basic
reproduction number, epidemic forecasting, and evaluation of control strategy.
Strikingly, the errors depend on the generation-to-removal time ratio but not
on the specific values and distributions of these times, and this universality
will further facilitate prediction rectification. Overall, our study provides a
general criterion for modeling memory-dependent processes using the Markovian
frameworks