key: cord-0867073-cffjmerr
authors: Zou, Zhuoru; Fairley, Christopher K.; Shen, Mingwang; Scott, Nick; Xu, Xianglong; Li, Zengbin; Li, Rui; Zhuang, Guihua; Zhang, Lei
title: Critical timing and extent of public health interventions to control outbreaks dominated by SARS-CoV-2 variants in Australia: a mathematical modelling study
date: 2021-11-18
journal: Int J Infect Dis
DOI: 10.1016/j.ijid.2021.11.024
sha: 3e63af92eb119647ff8f039d6301f2d13f64d063
doc_id: 867073
cord_uid: cffjmerr

Objectives The exact characteristics of a COVID-19 outbreak that trigger public health interventions are poorly defined. We aimed to assess the critical timing and extent of public health interventions to contain COVID-19 outbreaks in Australia. Methods We developed a practical model using existing epidemics data in Australia. We quantified the effective combinations of public health interventions and the critical number of daily cases for intervention commencement under various scenarios of changes in transmissibility of new variants and vaccination coverage. Results In the past COVID-19 outbreaks in four Australian states, the number of reported cases on the day that interventions commenced strongly predicted the size and duration of the outbreaks. In the early phase of an outbreak, containing a wildtype-dominant epidemic to a low level (≤10 cases/day) required effective combinations of social distancing and face mask use interventions to be commenced before the number of daily reported cases reaches 6 cases. Containing an Alpha-dominant epidemic would require more stringent interventions that commenced earlier. For Delta variant, public health interventions alone will not contain the epidemic unless with vaccination coverage of ≥70%. Conclusions Our study highlights the importance of early and decisive action in the initial phase of an outbreak. Vaccination is essential for containing variants.

The coronavirus disease 2019 pandemic continues to cause catastrophic health and economic crisis around the world (McKee and Stuckler, 2020; World Health Organization, 2021) . To prevent the consequences of the COVID-19 epidemic, 22 vaccine candidates have been approved by the World Health Organization (Craven, 2021 ). Yet, achieving global herd immunity with these vaccines will take time, given the existing disparity of COVD-19 vaccines across the globe (Forman et al., 2021) .

Non-pharmaceutical interventions remain the most effective means for COVID-19 control until herd immunity can be achieved. Non-pharmaceutical interventions have been successful in controlling the wildtype-dominant outbreaks in countries such as Australia, China, New Zealand, and Singapore in the past. These past experiences have demonstrated that early intervention results in more effective control of outbreaks.

However, the emergence of SAR-COV-2 variants with much stronger transmissibility has substantially changed the thresholds for public health interventions. For instance, the Alpha-dominant epidemic in the UK in late 2020 forced the government to elevate the tier 3 to tier 4 lockdown restrictions to combat its epidemic surge (Kirby, 2021) . In the most recent epidemics dominated by the Delta variant, two of the most populous Australian states, New South Wales and Victoria, have failed to revert the epidemic trend to achieve their original 'zero community transmission' target and resorted to policies of 'living with COVID-19' (Jose and Barrett, 2021) . In comparison, China and New Zealand have managed to contain the Delta-dominant epidemics to a very low level despite reports of sporadic cases. Understanding how timeliness and extent of public health intervention, taking into consideration of population vaccination coverage and variant transmissibility, would provide important evidence to explain the differences in COVID-19 control and epidemic severity in these countries.

Outbreak surveillance for early COVID-19 detection is essential to inform control measures. It enables stakeholders to commence interventions in time to avoid lengthy and extensive restrictions down the track and minimise health and economic losses.

Several studies have explored surveillance indicators for the early detection of COVID-19 outbreaks, such as COVID-19-related digital data streams and SARS-CoV-2 viral fragments detection in wastewater (Güemes et al., 2021; Hasan et al., 2021; Kogan et al., 2021) . In addition, modelling studies provide an early assessment of the severity of COVID-19 epidemics to help stakeholders act swiftly and decisively. Early projections of transnational spread of SAR-COV-2 influenced travel restrictions and border closures McBryde et al., 2020) .

Model projections based on the infectiousness of SAR-COV-2 demonstrated its pandemic potential, which guided the global response to and prepared countries for increases in hospitalisations and deaths (Liu et al., 2020; McBryde et al., 2020) .

Modelling studies that combined historical epidemiological data to project the trend and severity of COVID-19 epidemics for different policy decisions informed stakeholders about the potential effects of interventions before implementation (Koo et al., 2020; Moore et al., 2021; Panovska-Griffiths et al., 2020; Stuart et al., 2021) .

Models have played a non-negligible role in early outbreak surveillance and policy development. However, none of the previous modelling studies quantified the commencement time and extent of interventions when facing a COVID-19 outbreak of unknown severity and impact to the community. A predictive model that provides timely alerts for intervention commencement and the extent of interventions has great practical value in curbing COVID-19 outbreaks.

Our objective was to establish a predictive model to assist stakeholders in decision-making regarding timely and effective interventions based on limited surveillance data in the early stages of an outbreak. Building on previous models Zhang et al., 2020) , this model integrates existing public health interventions, population vaccination coverage, and the transmissibility of variants. It predicts the severity of the COVID-19 epidemic in the near future and quantifies the critical timing and extent of interventions to allow outbreaks to be contained. We selected Australia as a case study because it had developed a sophisticated COVID-19

surveillance system that reports the number of daily cases with a source of infection (i.e., whether a new diagnosis is linked to a known case) (Australian Government Department of Health, 2021a). This provides essential information to shed light on the extent of viral spread at the community level Moghadas et al., 2020) .

Our study finding would inform decision-making on interventions in Australia and is transferrable to other settings worldwide.

We collected COVID-19 epidemic data, including the number of daily reported cases (both with known and unknown sources), cumulative confirmed cases, and deaths based on official reports from the Australian Department of Health (25 January 2020-12 March 2021) (Australian Government Department of Health, 2021a). Satisfactory data from Victoria, New South Wales, the Australian Capital Territory, and Western Australia were collected for analysis, while other states and territories were not included due to a lack of detailed information on the source of confirmed cases (e.g., whether cases were from known clusters). We calibrated our model against the Victorian data (Appendix p11-12 and Figure S5 ). We used data from New South Wales, Australian Capital Territory, and Western Australia, for model validation (Appendix p17 and Figure S10 ). We collected relevant health policies and timelines 

We constructed a Susceptible-Infected-Recovered compartmental model ( Figure S1 ) based on published studies Zhang et al., 2020) to simulate the transmission of SARS-CoV-2 in the Australian population (parameters in Table S1 ).

We integrated the following five public health interventions in the model (Appendix p2-11).

Face mask use would reduce the probability of transmission in each exposure, which would be reduced by 75% (95% CI: 50-95%) in a single exposure with the presence of a face mask (Chu et al., 2020; Howard et al., 2021; MacIntyre et al., 2008) .

Social distancing would reduce the average number of daily contacts in public spaces.

Based on proportional deviations of real-time mobility from the pre-epidemic level in public places from 'Google COVID-19 community mobility data', we estimated the average number of daily contacts at various levels of social distancing restrictions.

Contact tracing enabled a proportion of all close contacts of confirmed cases to be quarantined and tested. Our model estimated that contact tracing in Australia would reach 80% of close contacts of the diagnosed individuals. Among the identified close contacts, approximately 20% of respondents were uncooperative, and 60% of recall information might be biased (Alsubaie et al., 2019; Dyani, 2020) .

Ideally, voluntary testing was given to individuals who believed they were in close contact with infected individuals and may be at risk of infection. We simplified this question by assuming approximately 0.09%-0.2% of the Australian population receiving voluntary testing daily, according to the reported cumulative number of COVID-19 voluntary tests over the past 7 days and the population size in Australia.

Vaccination would protect the portion of the population who receives the vaccine and develops an immune response. We estimated the population vaccination effectiveness to be about 82.2% by weighing the percentages for the supply of COVID-19 vaccines in Australia (Australian Government Department of Health, 2021b; Baden et al., 2021; Polack et al., 2020; Voysey et al., 2021) . We also assumed a 2% and 10% reduction in the efficacy of the existing vaccines against the Alpha and Delta variants (Lopez Bernal et al., 2021; Sheikh et al., 2021) .

Undocumented cases represented a potential risk of further community transmission of SARS-CoV-2. We defined 'undocumented cases' as asymptomatic infections, pre-symptomatic infections, and symptomatic infections before diagnosis. We explored the association between reported daily locally acquired cases and model-estimated potential undocumented cases in past Australian outbreaks and found significant linear relationships between them (Appendix p13-15 and Figure S6 -S9).

The basic reproduction number (R 0 ) represents the average number of secondary cases generated by a typical infectious case when it was introduced into a fully susceptible population (van den Driessche and Watmough, 2002) . We estimated R 0 to be 2.01 (1.91-2.21) in Australia, consistent with the previous findings (1.40-2.27) (Price et al., 2020; Rockett et al., 2020; Stapelberg et al., 2021) . The effective reproduction number (R e ) measured the actual transmissibility of an infectious disease in a population with the presence of public health interventions (Bo et al., 2021; Yabe et al., 2020) . We presented the time-varying R e of COVID-19 by the Australian state in Figure 1 (see Appendix p16, for the detailed derivation and calculation).

We assessed the risk of a COVID-19 outbreak by predicting the number of secondary cases potentially caused by undocumented cases over the next 7 days. First, we estimated R e (Figure 1 ), which represents the average number of secondary cases caused by a case during an average 14-days infectious period (i.e., the weighted period of the average interval from infection to isolation for symptomatic individuals and the average interval from infection to spontaneous recovery for asymptomatic individuals, Appendix p16). Second, the number of undocumented cases was estimated based on the daily number of unknown-source and known-source cases through the linear relationships ( Figure S8 ). Third, the overall number of secondary cases over the next 14 days was estimated by multiplying R e with the number of undocumented cases. Dividing it by two gave the estimate of the number of reported cases over a 7-day period.

We used the number of daily reported locally acquired cases as an indicator to inform the critical timing for intervention commencement. The turning point (peak) of the epidemic would occur approximately one week after the intervention commencement (Qiu et al., 2021; Triukose et al., 2021) . Besides, the number of daily reported cases would likely continue to rise until R e reduced below one. Therefore, during the time gap between intervention commencement and when R e fell below one, confining the number of daily reported cases to a manageable level (e.g. ≤10 cases/day) may avoid overloading the healthcare capacity and reduce impacts on economic activities. We defined the number of reported cases that would trigger intervention commencement to reduce R e to below one and maintain the average number of daily reported cases over a 7-day period into interventions below 10 cases to be the critical timing for intervention implementation (Appendix p17).

Probabilistic sensitivity analysis was conducted based on 1000 simulations to accommodate the uncertainty of model parameters and determine the 95% confidence interval of the reproduction number. In addition, multiple scenarios were established to explore the impact of the transmissibility of SARS-CoV-2 variants, vaccination coverage, and effectiveness of face mask.

We identified nine outbreaks in the four Australian states from 25 January 2020 to 12

March 2021 (Table 1 and Figure 1 -2). We observed that the reported cases on the day interventions commenced were highly correlated with the subsequent peak size and duration of the outbreak (Figure 2 ). Of the nine outbreaks, four times the state government intervened when the number of daily reported cases was below 10 cases, and the subsequent peak size of the outbreak was limited (1-10 cases), and the outbreak was contained within a month. In contrast, on four occasions, the state governments intervened when the number of daily cases was between 10-30 cases.

The subsequent outbreak peak was substantial (<100 cases), and the outbreak was contained within three months. On one occasion, intervening late at a daily reported case of 149 resulted in a very high outbreak peak of 687 cases and an outbreak duration of almost five months (Table 1 and Figure 1-2) . Based on the past outbreaks, we used 10 cases per day as a manageable threshold.

The interval between intervention commencement and reduction of R e to below one was reduced over time (Table 1 and Figure 1 ). In four recent outbreaks (after the second outbreak in Victoria, the most severe outbreak in Australia), R e was reduced to near or below one less than 7 days after the intervention commencement.

A surveillance interface was developed to predict the potential outbreak severity based on the current daily reported cases and the extent of public health interventions.

The first panel in Figure 3a illustrated how the combinations of various levels of reduction in social activity and face mask coverage might impact on R e under the baseline scenario (in a wildtype-dominant epidemic with contact tracing, voluntary testing, but no vaccination). We observed that reducing social activity by two-third of the pre-epidemic level or increasing face mask use to at least 77% would reduce R e to below the threshold curve of one. The second panel in Figure 3a demonstrated the projected average number of daily cases over the next 7 days based on various combinations of R e and the number of daily reported cases. It showed three distinct regions that reflect various epidemic severities. Region A, where R e ≥1, indicated an uncontrolled and expanding epidemic in the near future; Region B, where R e < 1 but the predicted average daily cases over the next 7 days would still exceed a manageable level (e.g. 10 cases/day), indicated a controlled epidemic with a substantial risk of resurgence; Region C, where R e < 1 and the predicted average daily cases over the next 7 days were <10 cases, indicated a controlled epidemic with a reducing risk of resurgence.

Figure 3b-j illustrated the trajectories of intervention change and the predicted outbreak severity for the above nine outbreaks, from the date of intervention commencement to the date R e dropped to one, to the date with a minimum R e , and to the date of easing intervention. On five occasions, the trajectory of the projected epidemic severity underwent a shift from region A to region B before moving to region C, suggesting a substantial risk of a large and long-lasting outbreak. In contrast, on the remaining four occasions, the trajectory of the projected epidemic severity shifted directly from region A to region C, suggesting a well-controlled outbreak.

These were consistent with the actual outbreak outcomes (Table 1 and Figure 1 ). The number of cases on the day intervention commenced largely determined whether the trajectory of epidemic severity would pass through region B.

We predicted the average number of daily cases over the first 7 days after interventions at various combinations of the number of daily reported cases and R e on the day of intervention commencement ( Figure 4 ). In the baseline scenario, if the goal is to contain the epidemic to an average of ≤10 daily cases over the next 7 days, the critical number of daily reported cases that should trigger interventions would be 6 cases.

If the transmissibility of the novel variants increased by 50%, 80%, 110%, and 140%, we observed a rising or even vanishing threshold curve of R e (R e =1, Figure 5 ). It indicated that more stringent combinations of social distancing and face mask use, even in combinations with vaccination, would be required to reduce R e below one.

With a 50% (estimated 40-80% (Davies et al., 2021; Fort, 2021 ; Institute of Social and Preventive Medicine, 2021) for the Alpha variant) increase in transmissibility, reducing social activity by 80% of the pre-epidemic level combined with mandatory masks (50% coverage) could reduce R e to one without any vaccination. The critical number of cases to trigger intervention commencement would be 4 cases to maintain the average number of daily cases over the next 7 days to ≤10 cases ( Figure 4 ). In contrast, with a 140% (estimated to be 60% (Mahase, 2021) higher for the Delta variant than the Alpha variant and 140% higher than the wildtype) increase in transmissibility, social distancing and face mask use alone would not be sufficient to reduce R e below one.

If COVID-19 vaccination coverage reached 30%, 50%, 70%, and 90% in a wildtype-dominant epidemic, we observed a substantial decrease in the threshold curve of R e (R e =1, Figure 5) . The curve would disappear if vaccination coverage exceeds 70%, indicating that social distancing and face mask use restrictions would no longer be necessary if 70% of Australians are vaccinated. However, in an Alpha-dominant epidemic, vaccination coverage would need to reach 90% for social distancing and mask use restrictions to be fully relaxed. In a Delta-dominant epidemic, combinations of vaccination with social distancing and face mask use restrictions were required to reduce R e to one. We found that at 30% vaccination coverage, it would be almost impossible to reduce R e below one in combination with existing public health interventions. At 50% vaccination coverage, very strict social distancing (reduced by 70-80% of the pre-pandemic level) combined with face mask use (more than 80%) would be still needed to reduce Re to below one. To keep R e below one, 70% vaccination coverage, combined with 40-50% reduction in social activities and 60-70% of face mask use, is necessary; and at 90% vaccination coverage, it would only require a moderate (40%) reduction in social activities or sustaining 60% face mask use alone.

In all wildtype and variants dominant epidemics, the critical timing for intervention commencement could be delayed with increasing vaccination coverage (Figure 4) . In a Delta-dominant epidemic with 70% vaccination coverage, the number of reported cases on the day of intervention commencement could not exceed 5 cases to maintain the average number of cases over the next 7 days to ≤10 cases. Sensitivity analysis demonstrated that the effectiveness of face masks might affect the vaccination coverage required to reduce R e below one in a Delta-dominant epidemic (Figure S11-S12). Assuming that Australia achieves the target vaccination coverage of 70% (Australian Government, 2021) , the ratio of Alpha to Delta variants would also influence the level of social distancing and face mask use required to reduce Re below one in mixed epidemics ( Figure S13 ).

Our study identified the critical timing and extent for commencing public health interventions to contain COVID-19 outbreaks in Australia. We found that in the past Australian outbreaks, the number of reported cases on the day interventions commenced was a strong predictor of the subsequent peak size and duration of the outbreaks. We demonstrated the critical timing and extent of intervention required to contain the outbreak to a manageable level in different scenarios of variant transmission and vaccination coverage. We indicated that in the early phase of an outbreak, containing the prospective epidemic to a low level (≤10 cases/day) required effective interventions to be commenced before the number of daily reported cases reaches 6 cases. Containing an Alpha-dominant epidemic would require more stringent interventions that commenced earlier. For Delta variant, public health interventions alone will not contain the epidemic unless with vaccination coverage of ≥70%. In this case, to maintain the prospective epidemic to a low level (≤10 cases/day) still required effective interventions to be commenced before the number of daily reported cases reaches 5 cases.

Our study developed a practical model to assist decisions for determining the critical timing and extent of interventions. To our best knowledge, this study is the first of its kind to integrate existing public health interventions and epidemic severity to quantify the risk of COVID-19 resurgence. Our study also quantified the impact of various potential changes in viral transmissibility and levels of vaccination on the timing and extent of interventions, which is an important consideration given the current epidemic of the Delta variant worldwide. Additionally, the model may be extended to demonstrate future epidemic trends resulting from various combinations of different levels of public health interventions commenced at different time points. Our study will provide stakeholders with intuitive recommendations on the optimal timing of changes in policy and effective combinations of public health interventions, thereby helping to design fit-for-purpose policies.

Our study confirmed that the early commencement of strong public health interventions is critical in containing a COVID-19 outbreak. Our findings are echoed in many outbreaks in other settings. For example, in the recent (August 2021) Delta-dominant outbreak in New Zealand, the government declared a Level 4 lockdown and mandatory face mask use interventions immediately after the emergence of 5 local cases, resulting in rapid containment of the outbreak within a month (Ministry of Health, 2021) . In the face of re-emerging community transmission of COVID-19, our study will provide timely alerts for stakeholders on intervention commencement and will be an important component of outbreak surveillance in Australia.

Our results are particularly relevant when facing the emergence of more transmissible SARS-CoV-2 variants. The Alpha variant has about 50% (range: 40-80%) higher transmissibility than the wildtype (Davies et al., 2021; Fort, 2021; Institute of Social and Preventive Medicine, 2021) . It has become dominant in the United States and many parts of Europe, leading to a rebound of the epidemic (Kirby, 2021; New and Emerging Respirator Virus Threats Advisory Group, 2020) . For this variant, our model predicts that stricter measures that include 80% reduction in social activities and 50% public face mask use would be necessary to contain the epidemic without vaccination, and these restrictions need to be implemented earlier when there are only 4 reported daily cases. In contrast, for the Delta variant, with 60% higher transmissibility than the Alpha variant (Mahase, 2021) , combinations of vaccination and other interventions would be necessary to contain it ( Figure 5 ). However, our study encouragingly illustrated that expanding COVID-19 vaccination is an effective way for COVID-19 control and socioeconomic recovery. Nevertheless, concerted efforts of other public health interventions are still necessary if high coverage of vaccination cannot be guaranteed in the short term or facing more transmissible new variants. Our study will continue to provide important information for timely changes in public health interventions to help stakeholders make the most appropriate decisions as more transmissible variants emerge and vaccination coverage continues to increase.

Our study has several limitations. First, we simulated historical epidemics based on four Australian states but excluding Queensland, which experienced a significant outbreak in March-April 2020. That is because the state's official reports did not include information on whether a diagnosed case is from a known or unknown source and hence cannot inform our model. Second, we did not consider environmental differences, which is likely to play a role and differ between states. Third, to the completion date of this study, reliable data on the transmissibility and mortality of the novel variants of SARS-CoV-2 and the effectiveness of the COVID-19 vaccine against new variants are still under investigation. Our study was conducted with limited availability of these data. Finally, we did not differentiate between the nature of the new cases. Further individual-based modelling studies are necessary to explore the impact of new cases of different nature on the severity of the outbreak.

Our study quantified, for the first time, the critical timing and extent of public health interventions that would effectively control an outbreak. It provides stakeholders with intuitive recommendations for taking early and decisive action and, therefore, has important implications for facilitating the achievement of the ambitious goal of rapid and complete control of the COVID-19 outbreak.

The authors declare no conflict of interest. 

No human subjects were involved in this work and therefore ethical approvals were not required for the development of this manuscript. 

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