Data collection
Data on the characteristics of patients with symptomatic COVID-19 in Shijiazhuang from 2 January to 14 February 2021 were from daily reports released by the Health Commission of Hebei Province (http://wsjkw.hebei.gov.cn/). These publicly available data included sex, age, district of residence, and information on several key epidemiological time points (dates of confirmed diagnosis, quarantine/isolation, and first positive nucleic acid test). These data also included information on family relationships among cases. From such information, we could identify whether the cases were from the same family. All data were extracted and entered into a structured database. The inclusion and exclusion criteria for the data collection are as following.
Inclusion criteria
COVID-19 symptomatic cases reported during 2 January to 14 February 2021 in Shijiazhuang were included.
Cases who were diagnosed as asymptomatic firstly and then show the relevant symptoms were also included.
All cases were diagnosed according to the Diagnosis and Treatment Protocol for Coronavirus Pneumonia (Trial Version 8).
Exclusion criteria
Infected persons with the absence of relevant information (age, sex, district of residence, etc.) were not included. Thus, due to the lack of relevant information, infected patients who were diagnosed as asymptomatic and did not show symptoms later (namely true asymptomatic infections) were not included.
Case definition
Cases were diagnosed according to the Diagnosis and Treatment Protocol for Coronavirus Pneumonia (Trial Version 8) from the National Health Commission of China. Clinical confirmed diagnosis refers to the symptomatic persons according to CT results and clinical symptoms after the first positive nucleic acid test. When an individual was tested with positive nucleic acid, he/she would be reported to health authorities but need to be confirmed by clinical diagnosis (ground-glass opacities in CT manifestation, consolidative opacity, clinical symptoms, etc.) to become a clinical confirmed case; otherwise, he/she would be categorized to an asymptomatic case. Based on the information from the daily epidemic reports, all confirmed symptomatic cases were classified as “immediately confirmed cases” or “later becoming symptomatic cases”. Immediately confirmed cases were those who were diagnosed soon after or at the same time as symptom onset. Later becoming symptomatic cases were those who were diagnosed with asymptomatic infection during the incubation period and subsequently developed symptoms. A “family cluster” was defined by two or more cases that were family members who lived together (such as parents and children), or as relatives who had contact before diagnosis.
Four stages of the implementation of interventions
To control the COVID-19 outbreak in Shijiazhuang, serial non-pharmacological interventions (NPIs) were implemented, such as lockdown of the city, suspension of public transportation, building of centralized isolation apartments, and nucleic acid testing for the whole city. The implementation of control activities was divided into four stages (stage 1: 2–5 January; stage 2: 6–9 January; stage 3: 10–19 January; stage 4: 20 January–14 February) based on the start dates of the three rounds nucleic acid testing.
During stage 1, interventions were mainly implemented in Zengcun, a town in Gaocheng District, in which the first case was reported on 2 January. On 3 January, massive nucleic acid testing was performed in Zengcun. On 5 January, the Xiaoguozhuang Village of Zengcun was officially closed.
During stage 2, the first-round of city-wide nucleic acid testing was implemented. On 6 January, serial interventions were performed in Shijiazhuang, such as school closure, suspension of public transportation, and cancellation of all public events. On 8 January, all residents were asked to stay home for 7 days (i.e., the lockdown).
During stage 3, the second-round of city-wide nucleic acid testing began in some residential communities on 10 January and ended on 14 January. To prevent environment-to-human-transmission, more than 20,000 residents of 12 villages in Zengcun Town, Gaocheng District left their homes and were placed in centralized quarantine at another location on 11 January (“distant centralized quarantine”), and these 12 villages were thoroughly disinfected. The residents were allowed to return to villages when the outbreak was under control. The construction of a centralized isolation place the Huangzhuang Apartment began on 14 January, and the first batch of houses was delivered on 17 January. On 15 January, the government declared that the lockdown would be extended to 20 January.
During stage 4, the third round of city-wide nucleic acid testing was performed from 20 to 22 January, during which home quarantine was maintained.
Statistical analysis
All confirmed symptomatic cases (including immediately confirmed cases and later becoming symptomatic cases) were included in the statistical analysis. The epidemic curves by the date of confirmed diagnoses and the dates of positive nucleic acid testing, the geographical distribution of patients in Shijiazhuang and Gaocheng District were plotted. A t-test was used to analyze the difference in the mean age of immediately confirmed cases and later becoming symptomatic cases. A χ2 test or Fisher’s exact test was used to compare other characteristics of these two groups.
Based on family cluster data, in which the transmission events and the interval between symptom onset could be clearly identified, the best gamma distribution of the serial interval was estimated using the maximum likelihood method. Within a family cluster, a case who developed symptoms 1 to 3 days after the date of symptom onset of the index case may be infected by an unidentified infector [9]. For sensitivity analyses, clusters with delayed detections of 0, 1, 2, and 3 days from the date of symptom onset between index and consecutive generations of cases were used to estimate the serial interval.
To estimate the incubation period, COVID-19 cases with clearly defined periods of possible exposure and date of symptom onset were selected. The period of possible exposure was defined as the days between the earliest possible exposure and the latest exposure. Three parametric distributions (Weibull, Gamma, and Lognormal) were used with the Hamiltonian Monte Carlo method for Bayesian inference to estimate the incubation period [10]. The Leave-one-out Information Criterion (LooIc) was used to evaluate the performance of the three models.
The geographical distribution of COVID-19 cases was presented using ArcGIS software version 10.5 (Environmental Systems Research Institute, Inc.). The statistical analysis and estimations of the serial interval and incubation period were performed with the rstan [11] and MASS [12] packages in R project version 4.0.2 [13].
SEIR+q model
To assess the impact of the changes in the incubation period and the influence of serial interventions on the COVID-19 outbreak of Shijiazhuang, the classical compartmental SEIR model (susceptible, exposed, infectious, and recovered) was extended to the SEIR+q model (Fig. 1), which contained three additional compartments (Shq, home quarantined susceptible; Ecq, centralized quarantined exposed; and Iq, isolated infectious), as described in the equations below and selected initial values (Additional file 1: Table S1) [8, 14,15,16,17,18,19]. The maximum likelihood method was used to estimate the two unknown parameters (Q, number of comprehensive quarantined persons per day; β, transmission velocity, number of susceptible persons infected by an infector per day).
$$ \frac{dS}{dt}=\omega {S}_q-Q-\frac{\rho_E\beta \left(\varepsilon E+I\right)S}{N}-\frac{\left(1-{\rho}_E\right)\beta \left(\varepsilon E+I\right)S}{N} $$
$$ \frac{dS_{hq}}{dt}=Q-\omega {S}_{hq} $$
$$ \frac{dE}{dt}=\frac{\left(1-{\rho}_E\right)\beta \left(\varepsilon E+I\right)S}{N}-\alpha E $$
$$ \frac{dE_{cq}}{dt}=\frac{\rho_E\beta \left(\varepsilon E+I\right)S}{N}-\alpha {E}_{cq} $$
$$ \frac{dI}{dt}=\alpha E-\eta I $$
$$ \frac{d{I}_q}{dt}=\alpha {E}_{cq}+\eta I-\gamma {I}_q $$
$$ \frac{dR}{dt}=\gamma {I}_q $$
The fitted model was used to simulate the effects of changes of four key parameters that correspond to different interventions (Q, the number of comprehensive quarantined persons per day; 1/α, incubation period; 1/ω, isolation period; ρE, probability of an exposed person being found and centralized quarantined) on the COVID-19 outbreak. The comprehensive quarantine measures (Q), which mainly influenced the number of quarantined susceptible people, included close contact tracking, home quarantine, and similar quarantine measures. The effectiveness of nucleic acid testing (ρE), which had a significant impact on the centralized quarantine of exposed people, was a function of the scale and speed of this test. Estimation of unknown parameters and simulation of different scenarios were conducted in R project version 4.0.2 using the deSolve package [20].