  In this paper, based on the Akaike information criterion, root mean square
error and robustness coefficient, a rational evaluation of various epidemic
models/methods, including seven empirical functions, four statistical inference
methods and five dynamical models, on their forecasting abilities is carried
out. With respect to the outbreak data of COVID-19 epidemics in China, we find
that before the inflection point, all models fail to make a reliable
prediction. The Logistic function consistently underestimates the final
epidemic size, while the Gompertz's function makes an overestimation in all
cases. Towards statistical inference methods, the methods of sequential
Bayesian and time-dependent reproduction number are more accurate at the late
stage of an epidemic. And the transition-like behavior of exponential growth
method from underestimation to overestimation with respect to the inflection
point might be useful for constructing a more reliable forecast. Compared to
ODE-based SIR, SEIR and SEIR-AHQ models, the SEIR-QD and SEIR-PO models
generally show a better performance on studying the COVID-19 epidemics, whose
success we believe could be attributed to a proper trade-off between model
complexity and fitting accuracy. Our findings not only are crucial for the
forecast of COVID-19 epidemics, but also may apply to other infectious
diseases.
