A model simulation on the SARS-CoV-2 Omicron variant containment in Beijing, China

Objective The Omicron variant of SARS-COV-2 is replacing previously circulating variants around the world in 2022. Sporadic outbreaks of the Omicron variant into China have posed a concern how to properly response to battle against evolving coronavirus disease 2019 (COVID-19). Methods Based on the epidemic data from website announced by Beijing Center for Disease Control and Prevention for the recent outbreak in Beijing from April 22nd to June 8th in 2022, we developed a modified SEPIR model to mathematically simulate the customized dynamic COVID-zero strategy and project transmissions of the Omicron epidemic. To demonstrate the effectiveness of dynamic-changing policies deployment during this outbreak control, we modified the transmission rate into four parts according to policy-changing dates as April 22nd to May 2nd, May 3rd to 11st, May 12th to 21st, May 22nd to June 8th, and we adopted Markov chain Monte Carlo (MCMC) to estimate different transmission rate. Then we altered the timing and scaling of these measures used to understand the effectiveness of these policies on the Omicron variant. Results The estimated effective reproduction number of four parts were 1.75 (95% CI 1.66–1.85), 0.89 (95% CI 0.79–0.99), 1.15 (95% CI 1.05–1.26) and 0.53 (95% CI 0.48 -0.60), respectively. In the experiment, we found that till June 8th the cumulative cases would rise to 132,609 (95% CI 59,667–250,639), 73.39 times of observed cumulative cases number 1,807 if no policy were implemented on May 3rd, and would be 3,235 (95% CI 1,909 - 4,954), increased by 79.03% if no policy were implemented on May 22nd. A 3-day delay of the implementation of policies would led to increase of cumulative cases by 58.28% and a 7-day delay would led to increase of cumulative cases by 187.00%. On the other hand, taking control measures 3 or 7 days in advance would result in merely 38.63% or 68.62% reduction of real cumulative cases. And if lockdown implemented 3 days before May 3rd, the cumulative cases would be 289 (95% CI 211–378), reduced by 84%, and the cumulative cases would be 853 (95% CI 578–1,183), reduced by 52.79% if lockdown implemented 3 days after May 3rd. Conclusion The dynamic COVID-zero strategy might be able to effectively minimize the scale of the transmission, shorten the epidemic period and reduce the total number of infections.


Introduction
The Omicron variant (B.1.1.529) of SARS-CoV-2 was first identified in South Africa and was classified as a variant of concern named Omicron by WHO on November 26th, 2021 [1][2] . More than 30 amino acid mutations were detected in the spike protein of Omicron, including 15 amino acid mutations located in the receptor-binding domain (RBD), which raises significant concerns about the increase in pathogenicity transmissibility and immune escape of this variant [3] . Although most countries had promoted vaccination, the epidemic has not been effectively alleviated or controlled. Since the variant emerged, a sharp increase in SARS-CoV-2 infections in all WHO regions has been observed, and as of 2022, the Omicron variant accounts for more than 98% of se-quenced samples in the UK and USA and more than 89% of sequenced samples globally [4][5] . This rapid growth in infections is probably due to the variant's increased transmissibility and its ability to evade immunity conferred by previous infection or vaccination [6][7][8][9] .
On the other hand, the disease severity of the Omicron variant has sparked extensive discussion and has profoundly affected public policies. Growing evidence has shown that Omicron-infected patients exhibit milder symptoms than those infected by the earlier variants [10][11][12][13][14][15][16] . Moreover, since the virus replicates in the upper respiratory tract, it causes less lung damage than prior variants. Several researchers believe that the high transmission rate with very mild pathogenicity of the Omicron variant may build herd immunity, giving hope for the end of the pandemic [17] . Meanwhile, the majority of countries have de- clared an end to the new coronavirus SARS-CoV-2 pandemic and completely emptied epidemic prevention measures. However, a fresh debate has erupted regarding that the Omicron variant can work as a natural vaccine. It is possible that the pathogenicity of the Omicron variant may be underestimated because of rising levels of herd immunity via previous infections and vaccinations [18][19][20] . Notably, the proportion of young patients was higher among those infected by the Omicron variant [21] , which may result in reduced pathogenicity. In addition, the impact of the Omicron variant is not attenuated by reduced pathogenicity, the healthcare system is still under enormous pressure because of the sheer volume caused by the high transmissibility [22] . Also, according to some experts, considering the Omicron variant as a natural vaccine is a dangerous idea. It creates complacency and is based more on pandemic fatigue and incapacity to do more than on current data and that the Omicron variant is not a vaccine; no matter how light it is, because this variant has resulted in deaths and hospitalizations [23] . If the variant is allowed to spread, then it may be mutated and also infect again, meaning the pandemic will persist for a long time. The virus is continually changing and finding new methods to spread. The more it spreads, the more likely it is to mutate and create new outbreaks of cases. It is therefore preferable to halt transmission and eliminate any potential for mutation [24] .
Since the first identification of the Omicron variant case on January 15th 2022, there have been sporadic transmission of the Omicron variant in Beijing, especially the outbreak in April 2022. In China, in order to balance the epidemic containment and the social life of residents, dynamic COVID-zero strategy is the guiding principle since August 2021, so the Beijing Center for Disease Control and Prevention (BJCDC) also adopted it to contain the epidemic quickly, including mass nucleic acid testing, travel restrictions, extensive contact tracing, epidemic control with health code, graded and adjusted management of communities according to risk levels [25] . To examine how dynamic COVID-zero strategy had affected the outbreak progression, a promising way to estimate its effectiveness is data-driven modeling: inferring effectiveness by relating the non-pharmaceutical interventions (NPIs) implemented in different scenarios to the course of the epidemic, as previous existing works [26][27][28] . Some studies have focused on investigating the effect of interventions deployed in Beijing after the outbreak in Xinfadi agricultural products (XFD) market, using modified susceptible-exposed-infectiousrecovered (SEIR) compartmental models, depending on the specific scenario [29] .
In this study, we mathematically simulated and projected transmissions of the epidemic in Beijing from April 22nd to June 8th in 2022, by altering the timing and scaling of these measures used to understand the effectiveness of these policies on the Omicron variant. Our results showed that the preparedness, timing and rigorous NPIs deployed during this outbreak were effective and successful.

Customized dynamic COVID-zero strategy in Beijing
Dynamic COVID-zero strategy, especially adopted by China to respond to SARS-CoV-2 the Omicron variant with higher transmissibility since August 2021, consists of a comprehensive set of measures to identify SARS-CoV-2 infections and stop any transmission chain, thus repeatedly zeroing local transmission [25] . Whether and for how long a COVID-zero policy can remain in place is questionable and every country should be prepared to chart its own path to transit from a pandemic to an endemic phase while accounting for local epidemiology, vaccination levels, population immunity, and the strength of health systems as recommended by the WHO [30] .
To this end, the BJCDC adopted customized dynamic COVID-zero strategy and separated the city as lockdown zone, control zone, precaution zone, in terms of epidemic risk level as shown in Supplementary materials. Each zone would not implemented for a long time, as long as the release conditions are met, the risk level will gradually decrease. However, once the new confirmed case or other risks occur again, the level of zone will be upgraded accordingly, reflecting the characteristics of dynamic and precise prevention and control.

Data of the epidemic
We collected the epidemic data from website announced by the BJCDC for the recent outbreak in Beijing from April 22nd to June 8th in 2022. The cumulative cases was up to 1807. Epidemiological trends of this outbreak is shown in Figure 1 . After June 8th, however, new cases were not under control. We considered it as an independent outbreak linked to a nightclub called "Tiantang ". Thus, we ignored the new cases after June 8th. The epidemic data included the daily number of confirmed cases, asymptomatic infections, and the number of asymptomatic infections transferred to confirmed cases, so the new daily reported infections can be recalculated. Besides, the important adjustments of policy was collected and we set four dates when important policies were promulgated. The first date is May 3nd when nucleic acid testing began to be free for residents, meanwhile, the city also conducted several rounds of mass nucleic acid testing. The second date is May 12th when working at home was advocated. The last one is May 22nd when the prevention measures strengthening was carried on in some areas.

The SEPIR model and initial setting
By incorporation of the pre-symptomatic infectiousness (P) state, representing the infectiousness before symptom onset of SARS-COV-2 into the classic SEIR model, we developed a modified SEPIR model. Transmission process between each compartment is shown in Figure 2 . In addition, the sizes of each compartment are functions of time t as below: In the equations, refers to transmission rate from I to S . refers to transmission rate between the state of P and I ( r = 0.55; 95%   CI: 0.46 -0.62), according to a previous study [31] . , , denote as latent period, pre-symptomatic period and infectious period, respectively.
To demonstrate the effectiveness of dynamic-changing policies deployment during this outbreak control, we modified the transmission rate into four, designated as 1 , 2 , 3 , 4 , according to four policychanging dates April 22nd to May 2nd, May 3rd to 11st, May 12th to 21st, May 22nd to June 8th, as shown in Table 1 . We adopted Markov chain Monte Carlo (MCMC) to estimate different transmission rate. Furthermore, incubation period was 3.2 (95% CI 2.9-3.6) days as mentioned in Backer et al. [32] . It consisted of D e and D p , we assumed it last at least 1 day, thus D p , denoted as transfer period between P to I, was 2.2 days. Then, D i , denoted as transfer period between I to R , was 1.4 days, which was determined by the speed of case confirming from practical experience. The effective reproduction number R t was calculated as = + [31] . The initiation date of simulation was set on April 22nd, 2022 with the parameters indicated in Table 2 . SEIPR: susceptible-exposed-infectious-recovered

Estimation of parameters in the SEPIR model
We assumed that the observed number of ascertained cases in which individuals experienced symptom onset on day d-denoted as x d -follows a Poisson distribution with rate = −1 −1 , in which −1 was the expected number of presymptomatic individuals on day (d − 1). We fit the observed data from April 22nd to June 8th in 2022. Thus, the likelihood function is We estimated 1 , 2 , 3 , 4 by MCMC with the delayed rejection adaptive metropolis algorithm implemented in the R package BayesianTools (version 0.1.7) [33] . We used a non-informative flat prior of Unif (0, 2) for 1 , 2 , 3 , 4 . We set a burn-in period of 40,000 iterations and continued to run 100,000 iterations with a sampling step size of 10 iterations. Estimates of parameters were presented as posterior means and 95% credible intervals from 10,000 MCMC samples. All of the analyses were performed in R (version 3.6.2).

Validation of our model simulation
To validate our modeling, we first simulated the epidemiological trend with both observed daily new cases ( Figure 3 A) and cumulative cases ( Figure 3 B). Then we employed Gelman and Rubin's approach to monitor convergence of MCMC sampling in estimation of 4 transmission rate 1∼4 . PSRF (Potential scale reduction factor) and MPSRF (Multivariate potential scale reduction factor) are evaluation metrics. In our model simulation, these two factors were both close to 1, indicating a good performance in convergence.
In order to prevent the spread of the Omicron variant and maintain residents life normally, the BJCDC dynamically implemented control measures on three key dates, therefore we segmented observed data sequence into 4 parts. The results of 4 estimated R t are 1.75 (95% CI 1.66 -1.85), 0.89 (95% CI 0.79 -0.99), 1.15 (95% CI 1.05 -1.26) and 0.53 (95% CI 0.48 -0.60), respectively, as shown in Figure 4 . After first measure was taken on May 3rd, nucleic acid testing was free for residents, R t reduced to less than 1.0. Then followed by a second policy-changing date May 12th, a slight increase occurred in the third stage, R t was above 1.0. It suggested that prevention measures were relaxed a little. The reason was due to cancelation of mandatory daily nucleic acid testing, therefore the hidden risk among infectious was growth. Eventually, in order to control the spread of the Omicron variant rapidly, on May 22nd, the BJCDC took a significant strict measure to lower down R t below 1.0.

Model simulation on policy implementation
To understand the importance of appropriate interventions, we first simulated scenarios that control policies were not implemented. The second policy effected on May 12th, however, was a relaxed one, thus we excluded it in simulation. We found that if no policy were implemented on May 3rd, till June 8th cumulative cases would rise to 132,609 (95% CI 59,667 -250,639), 73.39 times of observed cumulative cases number

Model simulation on the timing of implementation
It is generally agreed that early interventions would greatly affect the development of an epidemic than late. Here we tried to explore the impact by adjusting the timing of policy implementation by postponing 3 or 7 days. Additionally, we also simulated 3 or 7 days earlier than the origin date of policies implementation ( Figure 6 ). Compared to the reality, a 3-day delay of the implementation of policies on May 6th, May 15th and May 25th would led to increase of cumulative cases by 58.28%. A 7-day delay would led to increase of cumulative cases by 187.00%. Comparing with delay, taking control measures 3 or 7 days in advance would resulted in merely 38.63% or 68.62% reduction of real cumulative cases.
The simulation result suggested that although there was an impact of early implementation of policies, the impact of delayed policy im-  plementation may result in catastrophic outcomes of the epidemic, supporting the notion that the appropriate and a good timing of policy implementation is essential for a transmission control.

Model simulation on more stringent city wide lockdown
It is noteworthy that, compared to strict citywide lockdown, the BJCDC implemented very precise and timely updated interventions during this small-scale outbreak. To evaluate the influence of this strategy, we simulated the scenarios with citywide lockdown through reduced R t by 91.57% referring to a method adopted in the situation of citywide lockdown in Wuhan outbreak [31] . Thus, we simulated the citywide lockdown before and after 3 days according to the first effective policy date May 3rd. Firstly, as simulation result showed, if the city immediately took action on May 3rd, the cumulative cases would be 508 (95% CI 360-680), reduced by 71.89% of the actual number 1,807. If lockdown implemented 3 days before May 3rd, the cumulative cases would be 289 (95% CI 211-378), reduced by 84%. And if lockdown implemented 3 days after May 3rd, the cumulative cases would be 853 (95% CI 578-1,183), reduced by 52.79% ( Figure 7 ).

Discussion
With the stringent border control and steady rolling out of vaccination from the beginning of 2021, China become one of the countries that maintain no large scale community transmissions after the successful containment of the first wave of the COVID-19 before the Omicron variant, although several sporadic clusters initiated likely through imported routes were reported [34][35] . However, there have in 2022 been several multi-cluster outbreaks caused by the Omicron variant of SARS-COV-2 in China, alerting that the transmission and prevalence of the Omicron variant of SARS-COV-2 will continue in the next period of time. Current data indicate that the Omicron variant causes mild clinical symptoms and few severe cases and deaths. Despite possible lower lethal risks than previous variants, the Omicron variant may cause a higher community transmission, and consequently, a higher hospitalization load in the following months, which potentially overwhelm already exhausted health care systems across the world [36] . Besides, it has emerged during the meaning time of vaccination of many nations. Despite the previous variants that does not impede vaccine -induced immunity, most of the developed countries have been reporting the Omicron variant from their genomic sequencing continuously, a possible threat for the vaccines' effectiveness [37] . This can add to an emerging picture that the Omicron variant may be inherently more transmissible, immune escape, and infectious, even in fully vaccinated or previously infected people, which should put global communities in an alerting situation.
Based on the practice in China, the Omicron variant can be contained by a range of non-pharmaceutical interventions against SARS-CoV-2. To contain the highly infectious and immune evasive Omicron variant, additional NPI measures will be required to maintain the dynamic COVIDzero strategy. This policy, adopted by China to respond to SARS-CoV-2 variants with higher transmissibility since August 2021, consists of a comprehensive set of measures to identify SARS-CoV-2 infections and stop any transmission chain, thus repeatedly zeroing local transmission. To this end, the BJCDC adopted customized dynamic COVID-zero strategy according to characteristic of the Omicron variant.
In this study, we used an SEPIR model to simulate the Omicron variant transmission and effectiveness of customized dynamic COVID-zero strategy for a recent outbreak in Beijing, China. Our results suggested the strategy was able to effectively minimize the scale of the transmission, shorten the epidemic period and reduce the total number of infections. The lessons learnt and the experience gained during the transmission containment are useful for battling against the SARS-CoV-2 coronavirus. Based on our simulation, the outbreak would become out of control with 132,609 estimated infections under the assumption of the absence of any interventions than the 1,807 reported cases in the reality in Beijing. The simulation on delayed interventions showed that the total case number would also surge greatly. It is noteworthy that the Beijing CDC adjusted the containment strategies based on the real-time analysis of the up-todate epidemic. The customized dynamic COVID-zero strategy was effective to cut the community transmission of the Omicron variant in the city. An increment infections were predicted if a delay was happened compared to the number in reality, supporting the notion that early implementation is essential for COVID-19 containment, also in agreement with the conclusion in a study by Islam et al. based on a meta-analysis for 149 countries globally [38] . In addition, a model simulation by Oraby and Brauner et al. [39][40] on the effectiveness of government driven interventions concluded that timely adjustment of NPIs are essential as the effective strategies for COVID-19 containment. We also simulated and analyzed the impact of the most stringent citywide lockdown implemented during the beginning of the pandemic in Wuhan. Our data suggested that the implementation of city wide lockdown would reduce the scale of the outbreak to 508 cases (on May 3rd), a 71.89% reduction than the 1,807 real-world cases of reported in Beijing during the outbreak. As social cost is an essential element in consideration during an epidemic control, dynamic COVID-zero strategy are more practical to balance both purposes during the application.
In summary, dynamic COVID-zero strategy can effectively contain COVID-19 transmission caused by the Omicron variant. Under such strategies, mass nucleic acid testing and effectively strengthened and adjusted management of effected areas raised to the top selections as major policies, which are thought to contribute to the successful containment of several outbreaks from expanding to larger scales [41][42] . In addition, through mathematical modeling, we suggested that it is important to apply intervention in a timely manner. This is helpful not only as means to supplement the current COVID-19 epidemic prevention and control strategy in China, but also provides valuable experience for other countries around the world to optimize their COVID-19 outbreak prevention and control measures.
This study has some limitations. In our simulations, we assumed that resources were adequate and all the NPIs were effectively implemented even as the numbers of cases surged. In reality, as disease transmission increased, some resources (e.g., centralized quarantine facilities) would be depleted and eventually reach a shortage. We also only evaluated the magnitude of transmission in every scenario. Although it is important with respect to containment, they fail to take other factors into account and ignore other outcomes of interest. Further study should be conducted using this model to evaluate the NPIs in different ways. Finally, although we conducted a comprehensive literature search, the epidemiological characteristics of the Omicron variant, clinical severity, vaccine effectivenes (VEs) of primary and booster vaccination, as well as the effectiveness of antiviral therapies, are not fully understood. So expert judgement should thus be used to adjust specific implementation details. Many governments around the world seek to keep R t below 1.0 while minimizing the social and economic costs of their interventions. Beijing offers a customized dynamic COVID-zero strategy which is an example most in need of virus containment measures so that activities can continue as the pandemic develops. However, experts should adjust specific implementation details instead of taking it as a final word.

Conflicts of interest statement
The authors declare no competing interest.

Funding
This work was supported by the National Key R&D Program of China (Grant No. 2021ZD01144101).

Author contributions
Shihao Liang designed the study. Zhengyuan Zhou performed the research. Shihao Liang performed the statistical analyses. Tianhong Jiang and Zhengyuan Zhou wrote the initial paper.