A data-driven analysis on the mediation effect of compartment models between control measures and COVID-19 epidemics (preprint)

We make a retrospective review on various control measures taken by 127 countries/territories during the first wave of COVID-19 pandemic until July 7, 2020, and evaluate their impacts on the epidemic dynamics quantitatively. The SEIR-QD model, as a representative for general compartment models, is used to fit the epidemic data, enabling the extraction of crucial model parameters and dynamical features. The mediation effect of the SEIR-QD model is revealed by using the mediation analysis with structure equation modeling for multiple mediators operating in parallel. The inherent impacts of these control policies on the transmission dynamics of COVID-19 epidemics are clarified, and compared with results derived from both multiple linear regression and neural-network-based nonlinear regression. Through this data-driven analysis, the mediation effect of compartment models is confirmed, which provides a better understanding on the intrinsic correlations among the strength of control measures and the dynamical features of COVID-19 epidemics.

Rational evaluation of various epidemic models based on the COVID-19 data of China (preprint)

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 epidemics which is spreading worldwide right now. In this paper, 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 widely used in the literature. 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 errors and robustness index to quantify these three golden means and to evaluate various epidemic models/methods. Through extensive simulations, we find that the inflection point plays a crucial role in the choice of the size of dataset in forecasting. Before the inflection point, no model considered here could make a reliable prediction. 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 with the progression of epidemics 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 dynamical models based on ODEs, it is observed that the SEIR-QD and SEIR-PO models generally show a better performance than SIR, SEIR and SEIR-AHQ models on the COVID-19 epidemics, whose success could be attributed to the inclusion of self-protection and quarantine, and a proper trade-off between model complexity and fitting accuracy.

Rational evaluation of various epidemic models based on the COVID-19 data of China (preprint)

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.

Epidemic analysis of COVID-19 in China by dynamical modeling (preprint)

The outbreak of the novel coronavirus (2019-nCoV) epidemic has attracted world- wide attention. Herein, we propose a mathematical model to analyzes this epidemic, based on a dynamic mechanism that incorporating the intrinsic impact of hidden la- tent and infectious cases on the entire process of transmission. Meanwhile, this model is validated by data correlation analysis, predicting the recent public data, and back- tracking, as well as sensitivity analysis. The dynamical model reveals the impact of various measures on the key parameters of the epidemic. According to the public data of NHCs from 01/20 to 02/09, we predict the epidemic peak and possible end time for 5 different regions. The epidemic in Beijing and Shanghai, Mainland/Hubei and Hubei/Wuhan, are expected to end before the end of February, and before mid- March respectively. The model indicates that, the outbreak in Wuhan is predicted to be ended in the early April. As a result, more effective policies and more efforts on clinical research are demanded. Moreover, through the backtracking simulation, we infer that the outbreak of the epidemic in Mainland/Hubei, Hubei/Wuhan, and Wuhan can be dated back to the end of December 2019 or the beginning of January 2020.

Epidemic analysis of COVID-19 in China by dynamical modeling (preprint)

The outbreak of novel coronavirus-caused pneumonia (COVID-19) in Wuhan has attracted worldwide attention. Here, we propose a generalized SEIR model to analyze this epidemic. Based on the public data of National Health Commission of China from Jan. 20th to Feb. 9th, 2020, we reliably estimate key epidemic parameters and make predictions on the inflection point and possible ending time for 5 different regions. According to optimistic estimation, the epidemics in Beijing and Shanghai will end soon within two weeks, while for most part of China, including the majority of cities in Hubei province, the success of anti-epidemic will be no later than the middle of March. The situation in Wuhan is still very severe, at least based on public data until Feb. 15th. We expect it will end up at the beginning of April. Moreover, by inverse inference, we find the outbreak of COVID-19 in Mainland, Hubei province and Wuhan all can be dated back to the end of December 2019, and the doubling time is around two days at the early stage.