Materials and methods

Model
We employed an infectious disease dynamics model (SEIR model) for the purpose of modeling and predicting the number of COVID-19 cases in Wuhan, China. The model is a classic epidemic method to analyze the infectious disease, which has a definite latent period, and has proved to be predictive for a variety of acute infectious diseases in the past such as Ebola and SARS22,26–31. Application of the mathematical model is of great guiding significance to assess the impact of isolation of symptomatic cases as well as observation of asymptomatic contact cases and to promote evidence-based decisions and policy.
We assumed no new transmissions from animals, no differences in individual immunity, the time-scale of the epidemic is much faster than characteristic times for demographic processes (natural birth and death), and no differences in natural births and deaths. In this model, individuals are classified into four types: susceptible (S; at risk of contracting the disease), exposed (E; infected but not yet infectious), infectious (I; capable of transmitting the disease), and removed (R; those who recover or die from the disease). The total population size (N) is given by N = S + E + I + R. It is assumed that susceptible individuals who have been infected first enter a latent (exposed) stage, during which they may have a low level of infectivity. The differential equations of the SEIR model are given as:32,33\documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym} 				\usepackage{amsfonts} 				\usepackage{amssymb} 				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\begin{array}{l}{\mathrm{d}}S/{\mathrm{d}}t = - {\beta}\,{S}\,{I}/{N},\\ {\mathrm{d}}E/{\mathrm{d}}t = {\beta}\,{S}\,{I}/{N} - {\sigma}\,{E},\\ {\mathrm{d}}I/{\mathrm{d}}t = {\sigma}\,{E} - {\gamma}\,{I},\\ {\mathrm{d}}R/{\mathrm{d}}t = {\gamma}\,{I},\\ {\beta} = {R}_{\mathrm{0}}{\gamma},\end{array}$$\end{document}dS∕dt=−βSI∕N,dE∕dt=βSI∕N−σE,dI∕dt=σE−γI,dR∕dt=γI,β=R0γ,where β is the transmission rate, σ is the infection rate calculated by the inverse of the mean latent period, and γ is the recovery rate calculated by the inverse of infectious period.
R software (version 3.6.2) was applied for all the calculations and estimates in the current study.

Data collection and parameter values

Estimation of the epidemic trend assuming the prevention and control measures are insufficient
We first estimated the epidemic trend in Wuhan, China assuming the current prevention and control measures are insufficient. In this process, S was assumed to be the population of Wuhan City (11 million)15,34. The initial assumed number of cases caused by zoonotic exposure was 40 (I) according to Imai et al.’s9 estimation. We proposed E at 20 times of I in accordance with Read et al.13. R was set as 0. σ was set as 1/5.2 according to the latest article by Li et al.15, which calculated the mean incubation period of COVID-19 to be 5.2 days. Chen et al.6 calculated the average hospitalization period of 31 discharged patients to be 12.39 ± 4.77 days. Yang et al.24 calculated the median time from disease onset to diagnosis among confirmed patients to be 5. γ was accordingly set as 1/18 (ceiling of 12.39 ± 5 is 18). R0 was chosen based on Imai et al.’s9 estimation 2.6 (1.9–3.1) assuming 4000 (1000–9700) infections as of 18 January.

Estimation of the epidemic trend assuming the prevention and control measures are sufficient
This section discussed the scenario where the current prevention and control measures are sufficient. The set of S, E, I, R, σ, and γ is the same as the first section except that we also explored the model with E at 30 times of I to provide a possible range of number of infections. The absence of fever in COVID-19 cases is more frequent than in SARS-CoV and MERS-CoV infection35. Such patients may be missed since the current surveillance case definition focused mainly on fever detection. Accordingly, the possibility of E at 30 times of I cannot be excluded.
R0 in this section was chosen by phases. The first phase ranges from 1 December 2019 to 23 January 2020 and can be regarded as the early phase of the epidemic when a few prevention and control measures were implemented. R0 was set as 3.1 consistent with Imai et al.’s9 estimation of high transmission level. On 23 January 2020, airplanes, trains, and other public transportation within the city were restricted and other prevention and control measures such as quarantine and isolation were gradually established in Wuhan20. So, the second phase began on 24 January and Rt was set as 2.6 consistent with Imai et al.’s9 estimation of moderate transmission level. Second February was the last day of the extended Spring Festival holiday and Chinese authorities mobilized more medical resources to support Wuhan ever since36. The newly constructed hospital “Huoshenshan” came into service on this day37 and “Leishenshan,” mobile cabin hospitals several days later38. Also, more and more medical teams arrived in Wuhan. So the third phase began on 3 February and Rt was set as 1.9 consistent with Imai et al.’s9 estimation of low transmission level. All of these measures may need one longest incubation period to take effect. So, the last phase began on 16 February and Rt was set as 0.9 and 0.5, respectively, assuming the prevention and control measures are sufficient and effective to depict two different levels of effect of the measures in reducing transmission probability.