The model structure is displayed in Fig. 1. We stratify the natural infective process into four stages: susceptible individuals, exposed infected individuals in the incubation period, symptomatic infected individuals, and removed individuals (who either recovered or died). Susceptible individuals are those who have not been infected before and are vulnerable to infection, in which they would become exposed infected individuals. After an incubation period of 6·4 days for coronavirus,5 exposed infected individuals, if not isolated, will develop into symptomatic infected individuals. After a symptom-onset period of 3·8 days,6 symptomatic infected individuals, if not isolated, would be hospitalized and get tested. A proportion of hospitalized cases would die within an average period of 14·7 days (for non-survivors of coronavirus since hospitalization), and the rest recover within an average period of 18·2 days (for survivors of coronavirus since hospitalization).7 The individuals who recover are assumed to gain immunity and would not be infected again. In our model we assume that healthcare facilities like negative pressure isolation wards and personal protective equipment (PPE) for medical staff are abundant, so that no further infection would occur once infected individuals are hospitalized or isolated. To take asymptomatic cases into account, we assume 7·5% of cases would be asymptomatic before recovery,8 who will remain at the stage of exposed infected individuals and keep infecting others with the same infectiousness of symptomatic cases until being isolated or self-recovered.9 Before being reported, exposed infected individuals or symptomatic infected individuals are suspected cases.
After individuals are hospitalized, official reporting will be performed. Considering the average testing and official reporting speeds for Wuhan were different before and after January 27, 2020, we assume days required for reporting individual cases in China are 4·5 days and 2·8 days before and after January 27, 2020.6 For western countries, considering the difficulty in confirming unknown COVID-19 cases before the Wuhan outbreak, we assume the reporting rate would gradually lineally accelerate to 4·5 days by February 19, and then lineally accelerate to 2·8 days by March 8, to reflect a growth of public awareness and government response. Delays are accounted for between infection, symptom onset, hospitalization, and recovery, by dividing the corresponding processes into two compartments.10 Given the possibility of COVID-19 infection during the late incubation period, we assume cases would be infectious since the second phase of exposed infection.11
We integrate human mobility process into traditional SEIR model to consider daily human mobility, through which susceptible individuals, exposed infected individuals in an incubation period, and symptomatic infected individuals could be exported freely between regions from December 10, 2019 to January 23, 2020, the time of the shutdown in Wuhan. However, after the shutdown in Wuhan, we assume only susceptible individuals and exposed infected individuals could travel freely by precisely screening symptomatic infected individuals.
For governmental interventions, besides the estimation and drawing of region-specific time-variant reproduction numbers, we estimate rates of region-specific time-variant social distancing, work resumption, and isolation based on extended SEIR model by fitting random walk process containing 2000 operators to the real total confirmation data for each region.
Susceptible individuals could expand their social distancing to the extent that they would not be infected, at a social-distancing rate, and similarly, individuals who have social-distanced themselves could resume work at a work-resumption rate and become susceptible individuals again. Exposed infected individuals and symptomatic infected individuals could be isolated at a region-specific time-variant rate. Once isolated, we assume that the individual would not infect others any more. We set the isolation period as seven days, as per the guidance from Public Health England, who suggest that people with COVID-19-like symptoms should self-isolate themselves for a seven-days medical observation since the time of symptom onset.12 After isolation, if still do not recover, the isolated individuals will be hospitalized, tested, and reported. The asymptomatic cases could also be isolated through contact tracing. As Wuhan governmental interventions such as travel bans, social distancing, school and workplace closure, and contact tracing, mainly started on January 23, 2020.13 Thus, we assume no isolation or social distancing effects exist before January 23 for both China and Western regions. A comparison of the moving trend of these parameters has been done between the Wuhan level, the Chinese average level, the United States level, and the Western average level.
Data sources and processing
Previous studies reported that the Coronavirus firstly emerged in Wuhan, China in early December, 2019.14 Thus, for Wuhan, Hubei Province excluding Wuhan, and other provinces in mainland China, data outlining total daily confirmed cases of COVID-19 were collected from December 10, 2019 to May 1, 2020, from the National Health Commission of the People’s Republic of China15 and the Health Commissions of distinct provinces. For each selected Western country, data for the total number of daily confirmed cases were collected from the daily situation reports of the World Health Organization for the same period.16 These data were fit in the extended stochastic meta-population model to estimate the dynamic trajectories of region-specific time-variant parameters, which would be the base for further scenario simulations.
Daily human mobility data between Wuhan, Hubei Province excluding Wuhan, and other provinces in mainland China were collected from the Baidu Migration Platform.17 That from December 10, 2019 to January 1, 2020 was backwards inferred as 50% of the mobility on January 1, 2020, which is moderately lower than the huge migration flows during the Chinese Spring Festival at the beginning of 2020.
Daily human mobility data between 13 Western countries (Switzerland, Sweden, Austria, France, the United Kingdom, Germany, Spain, Italy, Norway, the Netherlands, Belgium, Denmark and the United States) and between Western countries and Wuhan, Hubei Province excluding Wuhan, and other provinces in mainland China are inferred from seasonal flight data in 2019 from the European Union’s air passenger transport report of 12 European countries and origin and destination flight survey data from the Department of Transportation of the United States.18,19
Mobility data between Chinese regions and Western regions have been further corrected before application. First, based on daily flight statistics reports from Flight Manager20, from January 21, 2020 to March 19, 2020, to reduce the threat of epidemic spread, foreign airline companies substantially decreased daily numbers of international inbound and outbound flights in China by 87% on average compared with the average level before January 21, 2020. Second, to control the growth of imported cases from abroad and avoid a second outbreak, the Civil Aviation Administration of China (CAAC) twice declared it would reduce the number of international flights, once on March 20, 2020 and again on March 26, 2020.21,22 This is estimated to have decreased the number of international flights into and out of China by 37% and 85%, respectively. Moreover, since March 16, 2020, to counter the spread of the novel coronavirus, the European Union passed a travel ban to restrict non-essential travel from non-EU countries into Europe,23 so the human mobility data between the United States and European countries after March 16, 2020 are assumed to be 1% of the original.
Trajectory predictions and scenario simulations
Trajectories of total reported cases, individuals infected but not hospitalized, new cases reported, total deaths, and new recoveries every day have been estimated for Wuhan, Hubei Province excluding Wuhan, and thirteen Western countries, from December 10, 2020 to June 26, 2020, not controlling for under-reporting. After controlling for under-reporting, two another trajectories of total reported cases and individuals infected but not hospitalized are estimated. The under-reporting rate of each country is based on a previous study which estimated under-reporting for China (24%) and numerous Western countries (Switzerland 22%, Sweden 6·3%, Austria 29%, France 5·1%, The United Kingdom 4·8%, Germany 25%, Spain 8·5%, Italy 7·3%, Norway 40%, The Netherlands 7·4%, Belgium 5·4%, Denmark 18%, and United States 13%).24
In the simulation part, we have simulated three scenarios. First, to understand whether the rigorous strategy of Wuhan is more effective in curbing the spread of the epidemic, we examine a scenario where Western governments, from several time-points, simultaneously carry out intervention strategies in the same way as Wuhan, which is calculated as the average level of Wuhan in social-distancing and suspected-cases isolation during the first month after the shutdown in Wuhan. Second, to understand the significance of controlling imported cases from abroad in containing the epidemic, we have simulated a scenario where Western countries, from several time-points, simultaneously close their borders completely and ban all inbound or outbound mobility. Finally, we have simulated a scenario where less non-pharmaceutical interventions are in effect in China or Western countries to see how the epidemic would grow naturally without interventions.
Considering the COVID-19 epidemic may be already spreading globally since December, 2019,25 the model was seeded with 2, 1, and 0·1 initial symptomatic infected individuals in Wuhan, Hubei Province excluding Wuhan, and in other Chinese provinces and Western countries on December 10, 2019, with twice the number of exposed infected individuals.