Rational evaluation of various epidemic models based on the COVID-19 data of China.

During the study of epidemics, one of the most significant and also challenging problems is to forecast the future trends, on which all follow-up actions of individuals and governments heavily rely. However, to pick out a reliable predictable model/method is far from simple, a rational evaluation of various possible choices is eagerly needed, especially under the severe threat of COVID-19 pandemics now. Based on the public COVID-19 data of seven provinces/cities in China reported during the spring of 2020, we make a systematical investigation on the forecast ability of eight widely used empirical functions, four statistical inference methods and five dynamical models. We highlight the significance of a well balance between model complexity and accuracy, over-fitting and under-fitting, as well as model robustness and sensitivity. We further introduce the Akaike information criterion, root mean square error and robustness index to evaluate various epidemic models/methods. Through extensive simulations, we find that the inflection point plays a crucial role in forecasting. We further notice the Logistic function steadily underestimate the final epidemic size, while the Gomertz's function makes an overestimation in all cases. Since the methods of sequential Bayesian and time dependent reproduction number take the non-constant nature of the effective reproduction number into consideration, we suggest to employ them especially in the late stage of an epidemic. 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. Towards the ODE models, the SEIR-QD and SEIR-PO models are shown to be suitable for modeling the COVID-19 epidemics, whose success could be attributed to the inclusion of self-protection and quarantine.