Evaluating the feasibility of containment strategy against Omicron variants, based on a spatially structured individual-based SARS-CoV-2 transmission modelOverview

Here, we use a spatially structured individual-based SARS-CoV-2 transmission model to evaluate the feasibility of containment strategy against Omicron BA.1 and BA.2 in a densely populated urban setting in China. In particular, the model was built upon prior work that was applied to reconstruct the containment of the Xinfadi outbreak in Beijing caused by the ancestral SARS-CoV-2 lineage [17]. The model was further expanded to incorporate Omicron-specific epidemiology, in terms of transmissibility, generation interval, and immune evasion properties. The model considers various levels of nonpharmaceutical intervention strategies to reflect enhanced outbreak response protocols that have been adopted in China over time. Finally, the model further incorporates up-to-date vaccination coverage to reflect the current (as of March 2022) and future level of population immunity in China.

Individual reproduction number and SARS-CoV-2 transmission as branching process

To simulate the spread of SARS-CoV-2 in the absence of NPIs, we start by seeding the population of interest with three infected individuals. Each individual i infected at time ti can either be classified as symptomatic or asymptomatic based on the age-specific asymptomatic rate [18] of SARS-CoV-2 Φasymp. For symptomatic infections, we assign the time delay from infection to symptom onset τincu by drawing from the incubation period distribution Pincu(τ) [19]. To simulate the transmission of SARS-CoV-2 at the individual level, in the absence of NPIs, we assign individual i’s reproduction number Ri (number of secondary infections caused by i), by drawing from a negative binomial distribution NB(R0, k), where the mean of the negative binomial distribution R0 is the basic reproduction number (population average of Ri), and k is the dispersion parameter of negative binomial distribution, capturing the heterogeneity of SARS-CoV-2 transmission (we provide R0 and k values specific for Omicron later in the “Omicron BA.1 and BA.2 sublineages” section). Therefore, individual i would cause a total of Ri secondary infections. We assume the shape of each infected individual’s infectiousness profile follows the distribution of the generation interval GI(τ). Thus, the timing of transmission τij from individual i to individual j ∈  is given by τij = tj − ti, where ti and tj are the i and j’s timing of infection, and τij is drawn from the generation interval distribution GI(τ). We recursively simulate the onward spreading of secondary infections through multiple generations until the 30th day after virus introduction or the daily number of infections reaches 10,000.

Population structure reflecting age-specific contact patterns, occupation, transmission setting, and spatially resolved mobility patterns

When transmission between primary infection i and their contact j occurs, we first generate the setting of the transmission event (home, workplace, or community) permissive by the occupation of the primary infector i. We then assign the age of secondary infection j based on the age-specific contact matrices and the transmission setting. We further probabilistically determine j’s occupation in accordance with their age based on the transmission setting and primary infector i’s occupation. Conditional on the transmission setting, the geographical locations of the residences of secondary infections were assigned based on the street/town level mobility network from aggregated mobile phone data provided by China Unicom, one of the leading mobile phone service providers in China (see the study by Wang et al. [17] for more details).

Nonpharmaceutical interventions (NPIs)

The details of the public health measures in response to local outbreaks in China have been previously described [20, 21]. As shown in Fig. 1, we categorize these measures into seven types: (i) symptom-based surveillance in healthcare facilities and communities; (ii) mask-wearing order in public places; (iii) routine screening for workers with risk of occupational exposure; (iv) systematic tracing, quarantine, and testing of close contacts; (v) lockdown of residential communities with detected infections; (vi) mass testing; and (vii) mobility restrictions based on regional risk levels. All intervention strategies are summarized in Fig. 1, of which symptom surveillance, mask wearing, and occupational screening are routine interventions implemented regularly, while contact tracing, community confinement, mass testing, and mobility restrictions are public health emergency response only conducted when new infections are detected. We modeled the impact of NPIs by emulating their effect on accelerating case detection and preventing new infections. The detailed implementations of each NPI into the transmission model has been previously described in the study by Wang et al. [17]. Below we give a brief description of each NPI:

Symptom surveillance: Individuals who present symptoms consistent with SARS-CoV-2’s clinical presentation during healthcare consultations at hospitals and local clinics would be considered as SARS-CoV-2 suspected cases and be provisionally isolated in designated facilities. At least 3 subsequent PCR tests for SARS-CoV-2 diagnostics would be conducted at the 1st, 3rd, and 7th day of isolation. If the suspected case is diagnosed by molecular tests, they would remain in hospital and be treated until the individual is fully recovered and no longer infectiousness. To heighten case detection through symptom surveillance, routine temperature checking is implemented in public spaces, such as workplaces, markets, shopping malls, subway stations, railway stations, and airports. Any individual with suspected symptoms of SARS-CoV-2 will be asked to seek medical attention.

Mask wearing: Mask wearing is required in public spaces, including hospitals, public transportation, markets, shopping malls, and entertainment venues.

Occupational screening: Routine PCR screening is conducted among individuals with occupations at risk of SARS-CoV-2 infection and/or in frequent contact with the general population, including staff at customs and border control, international ports, and quarantine locations; healthcare workers; individuals working in confined environments (e.g., institutions providing long term care and prisons); staff providing public services (e.g., public transportation, delivery, museums, and libraries); and workers in businesses and wet markets. The screening frequency is determined based on the occupational exposure risk and the screening population can be adjusted according to the actual situation.

Contact tracing: A close contact is defined as person who interacts with a confirmed or suspected COVID-19 case for the period from 4 days before to 14 days after the illness onset or with an asymptomatic carrier for the period from 4 days before to 14 days after collection of the first positive sample. Close contacts are further grouped into household contacts, work contacts, and community contacts based on their transmission setting. Epidemiological investigations to identify close contacts, including manual investigations (e.g., phone contact, interview) and electronic tracing (e.g., mobile apps, online databases), should be completed within 24 h. Centralized quarantine for at least 14 days is required for all close contacts with periodic PCR testing at the 1st, 4th, 7th, and 14th day of quarantine and the 2nd and 7th day after discharge.

Residential community confinement: The residential communities with detected infections are on lockdown at the block level until 14 days after the last case identification, with stay-at-home orders for all residents other than essential workers. Supplies of living necessities are provided by community workers. Three rounds of PCR screening are conducted as part of mass testing for all community residents at the 2nd, 8th and 13th day of lockdown, respectively.

Mass testing: Emergency mass testing in a targeted area is immediately activated when a new infection is reported. The geographical scope is usually determined according to the administrative division. Multiple rounds of testing are often conducted, and each round should be completed within 3 days. A 10:1 or 5:1 pooled sample approach is used to expand the PCR capacity and increase cost effectiveness.

Mobility restrictions: Unrestricted movement is allowed in low-risk areas, i.e., streets/towns with zero to one detected infection. The street/town is upgraded to moderate risk once it has reported more than one infection, with entertainment venues being closed and mass gatherings being prohibited. Residents in moderate risk areas are required to avoid unnecessary travel. A street/town with more than five infections will be upgraded to high risk with more stringent population mobility restrictions being implemented, where all public transportation within and in and out of the area will be suspended. Temporal lockdown is sometimes adopted in high risk areas, with all residents except for essential workers staying at home during lockdown. The street/town will be downgraded to low risk if no new infections are reported for 14 consecutive days, with mobility restrictions gradually lifted.

Fig. 1

Nonpharmaceutical interventions to contain COVID-19 outbreak in Beijing, China. A Public health response after the virus introduction. B Routine interventions and public health emergency response (PHER) to accelerate case identification and prevent onward transmission

Omicron BA.1 and BA.2 sublineages

Current (April 2022) evidence suggests the Omicron variant has significant fitness advantage over Delta and has replaced Delta to become the dominate variant globally. A household transmission study from Denmark has shown that the Omicron BA.1 variant is 17% more transmissible than the Delta variant [22] for unvaccinated individuals, while the BA.2 variant is 27% more transmissible than BA.1 [23]. Assuming that Delta’s basic reproduction number is 6.4 [24], then the basic reproduction numbers for BA.1 and BA.2 are 7.5 and 9.5 respectively. The generation interval, incubation period, overdispersion, and symptomatic proportion are assumed the same for BA.1 and BA.2. For unmitigated transmission, we assume Omicron variant transmission’s offspring distribution follows a negative binomial distribution with mean R0 and the dispersion parameter k = 0.43 [25]. We assume the mean intrinsic generation interval of Omicron to be the same as Delta (4.7 days) [26]. We assume the incubation period follows gamma distribution with a mean of 5.8 days and standard deviation of 3.0 days [19]. We hypothesize that the proportion of symptomatic infections Φsymp increases with age, with 18.1%, 22.4%, 30.5%, 35.5%, and 64.6% of infections (without vaccination) developing symptoms in groups aged 0–19, 20–39, 40–59, 60-–79, and 80 or more years respectively [18] (see Additional file 1: Table S1).

Vaccination coverage and population immunity

As of March 17, 2022, a total of 3.21 billion doses of SARS-CoV-2 vaccines have been administered in mainland China, including two inactive vaccines (CoronaVac and Covilo) and a viral vector vaccine (Convidecia) [15]. As of March 17, 2022, the vaccine coverage of the primary series is 87.9%, on top of which 45.7% of the population have received a booster shot [15]. The effectiveness of primary vaccination, homologous booster and heterologous booster in preventing infection (VEI), symptomatic disease (VEs), and onward transmission (VET) caused by the Omicron variants was taken from the estimates in the study by Wei et al. [27] and Cai et al. [28], either extracted from real-world studies or predicted based on neutralizing antibody titers (NATs), and summarized in Additional file 1: Table S2.

Since the containment strategy has been maintained in mainland China since the beginning of the pandemic, the proportion of the population who has been infected with SARS-CoV-2 remains extremely low nationally [20, 21, 29]. In this study, we ignore the effect of infection-induced immunity and focus on vaccine-induced immunity.

Scenarios of SARS-CoV-2 containment under different variants, levels of population immunity, and NPI strengths

To anticipate the feasibility of maintaining the SARS-CoV-2 local containment in mainland China in 2022, we evaluate an exhaustive combinatory of hypothetical scenarios along the dimensions of different Omicron sublineages, level of population immunity, and strength of NPIs.

Variant type

We consider both the Omicron BA.1 and BA.2 sublineages, as they account for the vast majority of the currently circulating variants. According to prior studies, Omicron BA.1 is 17% more transmissible than the previously circulating Delta variant, with the corresponding basic reproduction number R0 = 7.5 [22], while Omicron BA.2 has an increased transmissibility of 27% comparing to BA.1, with R0 = 9.5 [23].

Level of population immunity

We consider three immunization scenarios for the modeling analysis with the baseline immunization scenario assuming the primary vaccine coverage the same as that of New Zealand (as of September 20, 2022) with 0% booster coverage and two enhanced immunization scenarios (a homologous booster scenario and a heterologous booster scenario) assuming the primary and booster vaccine coverage the same as that of New Zealand (as of September 20, 2022, see Additional file 1: Fig. S3 [16]). The effectiveness of vaccination on preventing infection, symptomatic disease, and reducing onward transmission is described in Additional file 1: Table S2.

Intervention strategy

To assess the effectiveness of different containment strategies, we firstly set a baseline scenario with moderate intervention intensity. The NPI intensity is then gradually increased in the subsequent scenarios until we have enough confidence to achieve epidemic control. Under each scenario, we consider the following hypotheses: (i) infections are isolated immediately at the time of laboratory confirmation; (ii) isolation and quarantine are completely effective on preventing onward transmission; (iii) the sensitivity of PCR testing varies with time, following the estimates of the prior study [30]; (iv) PCR testing should be completed (from collection of samples to reporting of results) within 6 h [21]; (v) the protective effect of mask wearing against onward transmission and infection of SARS-CoV-2 is 9.5% and 18%, respectively [31, 32]; and (vi) all household contacts are immediately quarantined, while all work contacts and 70% of community contacts are quarantined with a mean time delay of 0.7 days. Details of each intervention scenario are described below. The intervention parameters are summarized in Table 1.

Level 0 (Baseline interventions): In our baseline scenario, we hypothesize that 33.3% of the symptomatic infections seek healthcare attention with an average delay of 3.7 days after symptom onset. We assume a moderate mask-wearing order, with 10% of individuals wearing masks in the workplace and 30% in the community. For occupational screening, we assume that high-exposure risk population (i.e., relative risk (RR) = 8 comparing to low-risk groups, 2.5% of the working-age population) are tested every 3 days; moderate-exposure risk population (i.e., RR = 2, 7.5% of the working-age population) are tested every 7 days. Emergency response, including contact tracing, community confinement, mass testing, and mobility restrictions, is triggered right after the identification of the first infection. Mass testing is conducted at the street/town level and must be completed within three days after the first infection being detected. Stringent or moderate mobility restrictions are implemented according to the risk level of each street/town based on the real-time assessment of local transmission risk. The hypothetical origin-destination mobility matrix depending on risk levels, is shown in Additional file 1: Table S3.

Level 1 (Level 0 + Enhanced symptom surveillance): Comparing to the baseline intervention scenario, we enhance the intensity of symptom surveillance, with the proportion of detectible symptomatic infections increased from 33.3% to 66.7%, and the mean time delay from symptom onset to hospitalization shortened from 3.7 days to 2.7 days.

Level 2 (Level 1 + Enhanced mask wearing): Comparing to level 1 intervention scenario, a more stringent mask-wearing order is considered, assuming 50% and 80% of individuals wearing masks in the workplace and in the community, respectively.

Level 3 (Level 2 + Enhanced occupational screening): Comparing to level 2 intervention scenario, the population of occupational screening is then expanded, with 5% of working-age populations (i.e., RR = 7.5) included in high-risk group and tested every 3 days, and 20% (i.e., RR = 1.875) included in moderate-risk group and tested every week.

Level 4 (Level 3 + Enhanced mass testing): Comparing to level 3 intervention scenario, we further enhance the intensity of mass testing, with the rounds of testing increased from 1 to 5, and the geographical range of testing expanded from the residential street/town of the detected infections to the whole district/county.

Level 5: (Level 4 + Enhanced mobility restrictions): Comparing to level 4 intervention scenario, mobility restrictions are further enhanced if the outbreak cannot be contained through previous efforts. In addition to the lockdown of high-risk regions, strict and moderate mobility restrictions are implemented in moderate-risk and low-risk regions, respectively. The hypothetical origin-destination mobility matrix depending on risk levels is shown in Additional file 1: Table S4.

Table 1 Intervention parameters of each scenario

We exhaustively explored all combinatory of two Omicron sublineages, three population immunity levels, and six NPI intensity levels, for a total of 36 scenarios.

Outbreak simulation

For each of the 36 scenarios described in the previous section, we seed outbreaks with three initial infections distributed according to population density [33]. Their ages and occupations are sampled from the demographical structures [34]. We first simulate the transmission chain in the absence of NPIs, based on a branching process described in the “Individual reproduction number and SARS-CoV-2 transmission as branching process” section. We simulate the transmission chain until either reaching the 30th day after the virus introduction or when the daily number of new infections exceeds 10,000. We then simulate the effect of NPIs through pruning the unmitigated chains of transmission by removing branches that would otherwise be interrupted by the corresponding NPIs of the scenario of interest. Details of the implementations of the simulation can be found in the study by Wang et al. [17]. We run 100 simulations for each scenario to capture the stochasticity of the transmission process. For each simulation, the following summary statistics are calculated: (i) the overall effective reproduction number (Reff), defined as the average of the individual reproduction number of each infection infected after the implementation of NPIs (We consider a containment strategy is feasible if the effective reproduction number could be suppressed below the epidemic threshold of 1 after the implementation of the NPIs); (ii) daily number of new infections by modes of detection; (iii) the 5-day moving average effective reproduction number (Rt) at day t, defined as the average individual reproduction number for a cohort of infections infected within the time window of day t till day t + 5; and (iv) the spatial distribution of SARS-CoV-2 infections at the street/town level. The branching process model is coded in Python 3.10. The statistical analyses and visualization are performed using R software, version 4.0.2.

Estimating effective reproduction number during the early phase of the Omicron BA.2 outbreaks in Pudong, Shanghai, and Jilin, Jilin

In Additional file 1: Fig. S4, we plotted the daily incidence of the Omicron BA.2 outbreaks in Pudong district, Shanghai and Jilin city, Jilin province. The vertical dashed lines indicate the timing of imposing lockdown in both locations. We estimated the epidemic growth rate before the lockdown (assuming exponential growth during this period) through fitting a linear regression to the incidence curve (in log scale) prior to the lockdown. The growth rate along with its uncertainties were estimated as the slope of the linear regression. Based on the estimated growth rates and the generation interval distribution (the “Omicron BA.1 and BA.2 sublineages” section), we estimated the effective reproduction number in Pudong and Jilin based on method proposed by Wallinga et al. for empirical generation interval distributions [35]:

$$_e=\frac^n_i\left(^_}-^_i}\right)/\left(_i-_\right)}$$

where Re denotes the effective reproduction number, r denotes the growth rate, yi denotes the relative frequency of the histogram of the discretized generation interval at daily resolution, and ai denotes the category bounds in such histogram.

Projection of the SASR-CoV-2 disease burden in mainland China under different hypothetical scenarios, based on the observed disease burden of the Omicron BA.2 wave in Hong Kong SAR, China

As of May 11, 2022, the Omicron BA.2 wave in Hong Kong, China have subsided in terms of SARS-CoV-2 infections and deaths (see Additional file 1: Fig. S1A). The government of the Hong Kong Special Administrative Region also reported detailed morbidity and mortality data of the Omicron wave stratified by age and vaccination status [14, 36], as well as the daily vaccine coverage by vaccination status (see Additional file 1: Fig. S1B [14]). The Laboratory of Data Discovery for Health at the University of Hong Kong used mathematical model to project the epidemic trajectory and final epidemic size including all infections not limited to those have been captured by the surveillance system [12]. Here, we synthetize this information together and provide two bounding estimates of the infection fatality ratio for each of the specific age group and population with a given vaccination status. Specifically, let’s denote cαν and dαν as the number of reported SASR-CoV-2 infections and deaths of age bracket α and vaccination status ν, where α could take the value of < 3 years, 3–19 years, 20-39 years, 40–59 years, 60–69 years, 70–79 years, and 80 years and older and ν could take the value of “Unvaccinated,” “CoronaVac 1 dose,” “CoronaVac 2 doses,” “CoronaVac 3 doses,” “Comirnaty 1 dose,” “Comirnaty 2 doses,” “Comirnaty 3 doses,” respectively [14]. We could calculate the crude case fatality ratio CFRαv by age α and vaccination status ν as:

Additional file 1: Fig. S1C [36] plotted the age-specific case fatality ratio by vaccination status for the Omicron BA.2 wave in Hong Kong. Unvaccinated individuals have the highest case fatality ratio across all age groups while individual who received 3rd doses of either the CoronaVac or the Comirnaty vaccines have the lowest. However, it’s unlikely that Hong Kong’s surveillance system were able capture all infections among the Hong Kong population during the Omicron wave. Modeling analysis matching the epidemic trajectory of the Omicron wave have projected 4.5 million infections out of the 7.4 million Hong Kong population, representing an approximate infection attack rate of 60%. In the meanwhile, there were only 1.1 million reported infections as of May 11, 2022, suggesting roughly 1 in 4 Omicron BA.2 infections were reported. If we denote iαν as the number of total infections of age bracket α and vaccination status ν, then we can express the infection fatality ratio of the corresponding population:

However, iαν was not directly observed. To overcome this, we first assume that the total number of infections is the same as model projected 4.5 million, i.e.:

Under one extreme scenario, we assume that the distribution of iαν across age α and vaccination status ν is the same as the distribution of cαν across age α and vaccination status ν. i.e., iαν ∝ cαν. Given that \(\sum__=4.5\) million, we can calculate \(_^l\) within age group α and vaccination status ν, where l denotes this bounding scenario. The age and vaccination specific infection fatality ratio under this scenario l can by estimated as:

The Hong Kong Government also reported daily number of populations who had received 1st, 2nd and 3rd dose by vaccine type and age group α prior to the Omicron wave (February 15th, 2022) [14], based on which we could calculate the population size pαν of age bracket α and vaccination status ν. Under another extreme scenario, we assume that the distribution of iαν across age α and vaccination status ν is the same as the distribution of pαν across age α and vaccination status ν. i.e., iαν ∝ pαν. Given that \(\sum__=4.5\) million, we can calculate \(_^u\) within age group α and vaccination status ν, where u denotes this bounding scenario. The age and vaccination specific infection fatality ratio under this scenario u can be estimated as:

One issue is that we could not directly calculate pαν for the unvaccinated, thus we further assume that the fraction of population who got infected with 1 dose of the CoronaVac is the same as those who hadn’t received any vaccination. Thus, we could calculate pαν for the unvaccinated as:

Then, we could estimate \(IF_^u\) across all age groups and vaccination status, including the unvaccinated individuals.

We assume that all vaccines (mostly inactivated) used in mainland China have the same vaccine effectiveness of CoronaVac. Give the infection rate, vaccination coverage, and the effects of antivirals listed in Additional file 1: Table S5 [12, 15, 16], we could project the total number of SARS-CoV-2 caused deaths based on the estimated infection fatality ratio. Given that \(IF_^l\) and \(IF_^u\) provides different estimates, and consequently different projections for the total number of deaths, we provide both \(IF_^l\) and \(IF_^u\) as the lower and upper bound of projections.