key: cord-0721348-2nclk8rz
authors: Steyn, Nicholas; Lustig, Audrey; Hendy, Shaun C.; Binny, Rachelle N.; Plank, Michael J.
title: Effect of vaccination, border testing, and quarantine requirements on the risk of COVID-19 in New Zealand: A modelling study
date: 2021-12-28
journal: Infect Dis Model
DOI: 10.1016/j.idm.2021.12.006
sha: 3ab260135f751b232d88f5cc295ae7b15b9baddd
doc_id: 721348
cord_uid: 2nclk8rz

We couple a simple model of quarantine and testing strategies for international travellers with a model for transmission of SARS-CoV-2 in a partly vaccinated population. We use this model to estimate the risk of an infectious traveller causing a community outbreak under various border control strategies and different levels of vaccine coverage in the population. Results are calculated from N = 100,000 independent realisations of the stochastic model. We find that strategies that rely on home isolation are significantly higher risk than the current mandatory 14-day stay in government-managed isolation. Nevertheless, combinations of testing and home isolation can still reduce the risk of a community outbreak to around one outbreak per 100 infected travellers. We also find that, under some circumstances, using daily lateral flow tests or a combination of lateral flow tests and polymerase chain reaction (PCR) tests can reduce risk to a comparable or lower level than using PCR tests alone. Combined with controls on the number of travellers from countries with high prevalence of COVID-19, our results allow different options for managing the risk of COVID-19 at the border to be compared. This can be used to inform strategies for relaxing border controls in a phased way, while limiting the risk of community outbreaks as vaccine coverage increases.

From April 2020 until September 2021, New Zealand pursued a COVID-19 elimination strategy [1] and, through a combination of strict border controls and snap lockdowns when needed, has limited community transmission of SARS-CoV-2 to very low levels. As a result, New Zealand has negligible infection-acquired immunity to COVID-19 [2] . Australia has also relied on international border controls and a strong public health response to keep incidence of COVID-19 very low. New Zealand's vaccination programme began in February 2021 and is exclusively using the Pfizer/BioNTech mRNA vaccine. As of early December 2021, over 90% of New Zealand's eligible population (aged over 12 years) are fully vaccinated [3] . . As vaccine rollout programmes in New Zealand and Australia have progressed, both countries have begun to transition away from strict elimination strategies to managing COVID-19 in the community, accompanied by a phased relaxation of travel restrictions.

During 2021, the Delta variant of SARS-CoV-2 has displaced other variants and become dominant in many countries, including India, the UK and USA -countries with which New Zealand has close travel links. Because of the increased transmissibility of the Delta variant, it is unlikely that countries will be able to reach complete population immunity (i.e. a reproduction number that less than 1 in the absence of any other interventions) via vaccination alone [4, 5] . Other public health measures will be needed to control the virus, although reliance on these will reduce as vaccine coverage increases.

These measures may consist of a mixture of border controls designed to reduce the risk of cases being seeded into the population, and community measures designed to enhance surveillance and reduce the potential for transmission.

Recent modelling has shown that the increased transmissibility of the Delta variant has largely nullified the reduction in risk of quarantine breaches gained from vaccination of international travellers and quarantine workers [6] . This means that strong border controls, including limits on travel volume and mandatory government-managed isolation for international arrivals, remain essential to prevent reintroduction of SARS-CoV-2 into populations until they are protected by high levels of vaccine coverage. Once vaccination rates are sufficiently high, it is likely that border controls can be gradually relaxed in conjunction with ongoing community public health measures [7] . To do this safely, it will be important to quantify the relative risk of community outbreaks under different sets of mitigation measures for international travellers arriving to at the border. These may include different combinations of government-managed isolation and quarantine (MIQ), self-isolation at home, and pre-departure and post-arrival testing requirements. Between 1 February and 15 September 2021, J o u r n a l P r e -p r o o f 83% of New Zealand's border related cases were detected in the first 7 days after arrival and 75%

were detected in the first 5 days. This suggests that a reduced quarantine period of less than 14 days would catch the majority of cases, but other measures such as home isolation and follow-up testing after completion of quarantine testing may still be needed. Different sets of requirements could be applied to travellers depending on their risk profile, for example more stringent restrictions for people travelling from countries with high infection rates.

New Zealand has primarily used polymerase chain reaction (PCR) tests for SARS-CoV-2 testing throughout the pandemic, sometimes referred to as the gold standard test because of its high sensitivity. Around the world, countries are increasingly complementing PCR testing with lateral flow tests, also known as rapid antigen tests. These have lower sensitivity than PCR tests, particularly in the early and late stages of the infectious period [8, 9] . However, they have the advantage that they return results very quickly (typically within 30 minutes), they are cheap, and they do not require laboratory processing. This means they can be used to test large numbers of people at high frequency (e.g. daily) without stretching laboratory capacity and with fast turnaround of results.

Travel volume is a key determinant of the risk posed by international travel. As a consequence of limited MIQ capacity and citizenship or residence requirements for entry, the volume of international arrivals to New Zealand has been approximately 2% of pre-pandemic levels (with the exception of arrivals from Australia during limited periods of quarantine-free travel). It is important to factor this into risk evaluations because if, for example, a given mitigation provides a 10-fold reduction in the risk per traveller, this will be offset if there is a simultaneous 10-fold increase in travel volume.

In this paper, we use a stochastic model of SARS-CoV-2 transmission and testing to compare the relative reduction in transmission potential from infected travellers under various mitigations and at different levels of vaccine coverage in the resident population. This paper is a policy-oriented application of the model developed by [4] to investigate the potential impact of COVID-19 at different stages in New Zealand's vaccination programme.

The model allows for different effectiveness of isolation under different circumstances, for example MIQ versus self-isolation at home during asymptomatic, pre-symptomatic, symptomatic or confirmed stage of infection [10] . We compare different testing requirements, such as daily lateral flow tests (LFT) or less frequent PCR tests, allowing for the different sensitivity of these tests. The model also includes individual heterogeneity in transmission rates and the probability of returning a positive J o u r n a l P r e -p r o o f result if tested. We use the model to simulate community outbreaks seeded by international arrivals and calculate the probability that such an outbreak meets various pre-defined criteria. The aim is not to identify vaccination targets at which borders can be completely reopened, but rather to support evidence-based strategies for relaxation of travel restrictions by comparing the risk reduction from various policy options.

The modelling approach is similar to that of [11] , which estimated the reduction in transmission potential from a range of traveller interventions. The model of [11] modelled individual heterogeneity in viral load trajectories and assumed that the transmission rate and the probability of testing positive are both functions of the viral load. This requires that there is a unique one-to-one mapping between the transmission rate at time and the probability of testing positive at time . We found it difficult to reconcile this with the fact that there is significant pre-symptomatic transmission of SARS-CoV-2 and that the likelihood of individuals testing positive whilst pre-symptomatic stage appears to be significantly lower than after symptom onset. We therefore take a simpler approach based on an empirically estimated generation time interval and test positivity curve and we investigate the qualitative effects of different forms of heterogeneity in these.

In this section, we first define the stochastic age-structured model for transmission of SARS-CoV-2.

This model includes the effects of vaccination and case-targeted controls (case isolation and contact tracing) once a border-related community outbreak is detected. We describe the model for different interventions that can be applied to international travellers and how these affect potential transmission from international arrivals into the community. We then describe the testing model, defined in terms of the sensitivity of PCR tests and of LFTs as a function of time since infection. Finally, we describe how international travellers, under a given set of border interventions, are used to seed the community transmission model and define the simulation outputs that are calculated.

We model transmission of SARS-CoV-2 in the community using a stochastic age-structured branching process model in partially vaccinated population [4] . Vaccine allocation is assumed to be static (i.e. we J o u r n a l P r e -p r o o f do not consider simultaneous dynamics of community transmission and an ongoing vaccination programme). We assume that 90% of those over 65 years old are vaccinated and consider different levels of vaccine coverage in the 12-64 year age band (70%, 80%, 90%). For simplicity, we assume all individuals are either fully vaccinated or non-vaccinated (i.e. we do not consider the effect of people who have had a single dose). We assume the vaccine prevents infection in = 70% of people, and reduces transmission by = 50% in breakthrough infections. This provides an overall reduction in transmission of 85% [12] . We assume that breakthrough infections and primary infections are equally likely to cause symptomatic disease. This does not preclude breakthrough infections having a lower probability of severe illness or death, although we do not investigate these outcomes in this study.

Infected individuals are categorised as either clinical or subclinical, with the clinical fraction increasing with age [13] (see Table 1 ). Subclinical individuals are assumed to be = 50% as infectious as clinical individuals [14] . The incubation period is assumed to be Gamma distributed from infection time with mean 5.5 days and s.d. 3.3 days [15] . In the absence of interventions, we assume generation times follow a Weibull distribution with mean 5.0 days and s.d. 1.9 days [16] . There is at present conflicting evidence in the literature as to whether the Delta variant of SARS-CoV-2 has a shorter mean generation time or mean incubation period than other variants [17] [18] [19] [20] [21] . Generation times are difficult to empirically measure because this requires the infection times of both cases in a transmission pair.

If infection times are unavailable but symptom onset dates are known, the serial interval can be used as a proxy for generation time. However, serial interval measurements contain more noise as they depend on both individuals' incubation periods. In addition, observed generation times and serial intervals are affected by interventions such as test, trace and isolate measures. To investigate the effect of some of these uncertainties, we perform a sensitivity analysis with a shorter generation time (mean 2.9 days, s.d. 1.9 days) and incubation period (mean 4.4 days, s.d. 1.9 days) [20] .

Transmission between age groups is described by a next generation matrix. The ( , ) entry of this matrix is defined to be the expected number of secondary infections in age group caused by an infected individual in age group in the absence of interventions and given a fully susceptible population:

where is the relative susceptibility to infection of age group [14] , is a contact matrix describing mixing rates between and within age groups [22] Each individual is assigned a relative transmission parameter that is gamma distributed with mean 1 and variance 1/ . This allows for individual heterogeneity in transmission [24] . We set = 0.5, consistent with estimates of the overdispersion of SARS-CoV-2 in New Zealand and internationally [25, 26] . Under the assumptions about transmission between age groups and vaccine effectiveness and to the vaccinated class with probability . To account for the effect of vaccination in preventing infection, the putative secondary infections in the vaccinated class are thinned with probability . Immunity from prior infection is ignored in the model. This is reasonable because we only consider small community outbreaks and our model is applicable to populations, such as New Zealand and Australia, that have not yet experienced large-scale epidemics

We use a simplified model for case-targeted controls in the community. We assume there are initially no controls in place in the period of time before the outbreak is detected (i.e. before the first positive test result is returned). Outbreaks can be detected either via a positive test result in the infected traveller or by community testing. During the period before the outbreak is detected, we assume that symptomatic individuals in the community are tested with probability , = 0.12. This value is based on previous findings that, during a period with no known community transmission of SARS-CoV-J o u r n a l P r e -p r o o f findings were derived from an estimate of the number of people with Covid-like symptoms made using FluTracking data [28] . Once an outbreak has been detected, symptomatic testing rates typically increase significantly [27] . We therefore assume that all existing and subsequent clinical cases in the outbreak are detected with probability , = 0.4. In all cases, there is a delay from symptom onset to the test result being returned, which we assume to be exponentially distributed with mean 4 days [29] . To model the effect of contact tracing, we also assume that, after an outbreak is detected, all infected individuals are traced with probability = 0.7 and isolated with a mean delay of 6 days after infection (see Table 1 ). Table 1 . Model parameter values. *Susceptibility for age group is stated relative to susceptibility for age 60-64 years.

We model the effects of alternative sets of interventions on the expected transmission from an infected traveller. We use ( ) to denote the transmission rate of individual at time under a given intervention , relative to their unmitigated transmission rate at time . When ( ) = 1, this means individual is not quarantined or isolated at time ; when ( ) = 0, this means individual is fully isolated at time and cannot transmit the virus. Note that ( ) is also defined to be zero if individual

has not yet arrived at their destination, or has been prevented from travelling from pre-departure symptom checks or testing. The expected number of secondary cases caused by individual under interventions relative to no interventions is given by:

where ( ) is the probability density function for the generation time distribution.

Interventions can be split into three categories: vaccination requirements, pre-departure tests, and post-arrival restrictions. We consider a few key policies for each category in Table 2 . All scenarios assume a baseline level of screening of air passengers so that 80% of travellers who develop symptoms prior to departure are prevented from travelling, independent of any testing requirements. Figure 1 shows a schematic diagram of the model with the different pathways travellers can take through the border control system. J o u r n a l P r e -p r o o f Self-isolation after arrival can occur for any one of four reasons:

1. Due to a requirement to self-isolate while asymptomatic, assumed to reduce transmission to ( ) = .

2. Due to onset of symptoms, assumed to reduce transmission to ( ) = , regardless of the border policy. Isolation is assumed to begin on the day following symptom onset. This represents a situation where recent arrivals are contacted by public health teams to encourage monitoring of symptoms.

3. Due to return of a positive test, assumed to reduce transmission to ( ) = , regardless of the border policy. Isolation is assumed to begin on the day following the return of a positive result.

4. Due to a requirement to enter MIQ. For simplicity, we assume there is no risk of transmission between travellers in MIQ facilities ( ( ) = = 0). Transmission between travellers in MIQ facilities is known to have occurred [30, 31] , but this risk is likely to be much smaller than the risk of transmission from individuals in self-isolation at home.

Individuals isolate with the effectiveness of the strongest measure that applies at time . In all scenarios, we assume that self-isolation prevents 100% of transmission from confirmed cases ( ( ) = ). Self-reported adherence to requested quarantine measures in a Norwegian study was 71% of those with COVID-19-compaible symptoms and 28% of those without [10] . In the base scenario, we assume that self-isolation prevents 60% of transmission for travellers who are asymptomatic or pre-symptomatic ( = 0.4), and prevents 80% of transmission for travellers who are symptomatic but have not yet received a positive test result ( = 0.2). We also perform a sensitivity analysis where self-isolation is less effective than in the base scenario ( = 0.6 and = 0.4).

This formulation assumes that all isolated individuals transmit at a reduced rate . However, we expect average model outputs to be very similar if we instead assumed that a fraction of isolated individuals transmit at the same rate as a non-isolated individual and a fraction 1 − do not transmit at all [11] .

Individuals that develop symptoms after arrival seek a test with probability 80%. This test is assumed to be a PCR test taken with an exponentially distributed delay with mean 2 days after symptom onset and the result is returned the following day. If the individual is scheduled for any kind of test on the same day, they do not take the additional test.

The probability of testing positive is modelled as a function of time since infection. For RT-PCR tests we use data from [32] , with a peak probability of testing positive of 81% eight days after infection ( Figure 2 ). We construct a similar function for the probability of testing positive by LFT based on data from [33] . These results showed that 24 out of 25 individuals tested returned a positive LFT on the day after first positive culture of the virus from a nasal swab. However, real-world test performance is likely to be lower than in a controlled laboratory study. We therefore scaled the data from [33] so that the peak probability of testing positive was 73% (which is 90% of the PCR peak). We assumed that the peak occurs at the same time as the peak for the PCR test, i.e. eight days after infection (see Figure 2 ).

In addition, we assume that it is not possible to test negative by PCR and positive by LFT on the same day. To generate an LFT result, we therefore simulate the result of a putative PCR test where probability of a positive result is as shown by the blue curve in Figure 2 . If the putative PCR result is negative, we assume the LFT result is also negative. If the putative PCR result is positive, we assume the LFT result is positive with probability ( + | + ) = + ( )/ + ( ), which is the ratio of the red curve to the blue curve in Figure 2 .

J o u r n a l P r e -p r o o f Note that, although the peak sensitivity of the LFT is assumed to be 90% of the peak sensitivity of a PCR test, the overall sensitivity of the LFT is lower than this because of the faster decay away from the peak ( Figure 2 ). Under the model assumptions, a PCR test taken on a random day in the one week or two weeks following symptom onset will detect 77% or 66% of infected individuals respectively, relative to 60% or 33% of infected individuals respectively for a LFT. Although precise characterisation of time-dependent test performance is difficult, this is broadly consistent with results showing that LFTs detected between 40% and 80% of PCR-positive cases [34, 35] [36] [9, 37] . However, we also investigate a sensitivity analysis in which the peak sensitivity of the LFT is only 57%, which is 70% of the peak sensitivity of a PCR test (see Table 1 for time-dependent probabilities).

The probability of testing positive is assumed to be the same for subclinical and clinical individuals.

Conditional on being infected, the probability of testing positive is assumed to be the same for vaccinated as for non-vaccinated individuals. It is clear from Figure 2 that, under these assumptions, a significant amount of transmission occurs before the infected person has a high probability of testing positive. This may seem pessimistic but it is consistent with the fact that pre-symptomatic transmission of SARS-CoV-2 is known to be common and with empirical data showing that the probability of testing positive prior to symptom onset is J o u r n a l P r e -p r o o f much smaller than after symptom onset [32] . We also perform a sensitivity analysis to investigate the consequences of shifting the probability curves in Figure 2 to the left by 2 days.

For each set of interventions , we run = 100,000 simulations, each initialised with one infected traveller. The traveller is assigned an age-group with a frequency proportional to the New Zealand age-structure, an infection time uniformly randomly distributed in the 14 days prior to arrival, and a clinical status that depends on age. The simulation returns the transmission potential of the infected traveller ( ) and a list of any infections in the community. From these simulations, we report three model outputs defined as follows.

Output (1) To implement this model, we assume 1 is gamma distributed with mean 1 and variance 1/ * , and 2 is normally distributed with mean 1 and varaicne 2 truncated to non-negative values. If we set * =

(1 + 2 )/(1 − 2 ) then, provided 2 is sufficiently small, the product 1 2 is approximately gamma distributed with mean 1 and variance 1/ , as for the base model. We assume that the odds of testing positive are proportional to 2 and so we set the probability that a test on individual at time returns a positive result to be Table 3 shows the relative transmission potential of an average infected traveller under a given border policy. All results are relative to the same baseline, representing the transmission potential of a nonvaccinated traveller that faces no interventions other than a pre-departure symptom check.

Conditional on being infected, a vaccinated individual is assumed to be 50% as infectious as a nonvaccinated individual (Table 1) . Vaccinated individuals are less likely to be infected than nonvaccinated individuals. However, we do not attempt to model the epidemic dynamics in the traveller's country of origin so the results do not capture this effect.

Regular post-arrival symptom checks and isolation for symptomatic travellers (assumed to be 80% effective from the day following symptom onset) reduces the transmission potential to 78% of the baseline (unmitigated) transmission potential for non-vaccinated travellers and 39% for vaccinated travellers.

J o u r n a l P r e -p r o o f Requiring pre-departure testing reduces transmission potential only slightly (for vaccinated travellers from 39% with no pre-departure testing to 38% for PCR on day -3 or 36% for LFT on day -1). Although pre-departure testing and symptom checks screen out a significant fraction of infected travellers (approximately 34% for symptom-checks only, 54% with the addition of either test), many of these travellers would have been towards the end of their infectious period by the time they arrived at their destination. This explains why the reduction in transmission potential is relatively modest. The small difference between the effect of a PCR test on day -3 and a LFT on day -1 suggests the reduced sensitivity of the LFT is roughly offset by the fact it can be performed closer to the time of departure.

Of the post-arrival testing strategies, a daily LFT for 5 days is more effective (reducing transmission potential from 39% to 22% for vaccinated travellers) than PCR tests on day 0 and day 4 (39% to 33%).

This shows that, under the assumed test characteristics, the lower sensitivity of LFT tests is outweighed by the increased frequency of testing and faster return of results.

Adding a requirement for five days self-isolation after arrival further reduces transmission potential (from 33% to 15% with the PCR testing strategy and from 22% to 10% with the LFT strategy, for vaccinated travellers). Finally, a seven-day stay in MIQ with two PCR tests reduces transmission potential to approximately 0.2% for vaccinated travellers, and a fourteen-day stay in MIQ with two PCR tests reduces the transmission potential to a negligible level. Note that the model does not attempt to include the risk of transmission within MIQ facilities. 

The probability of onward transmission following a 7-day MIQ stay is between 0.5% and 1% depending on vaccine coverage in the population.

The LFT-based strategies also perform better than the corresponding PCR strategies at reducing the probability that an infected traveller transmits the virus without ever being detected by testing ( Tables 6 and 7 show the probability that an infected traveller starts an outbreak that causes at least 5 infections and at least 50 infections respectively (model output 2.iii and 2.iv). Comparing Tables 6 and   7 reveals that, in a non-vaccinated population, most outbreaks that reach 5 infections also go on to reach 50 infections, as the respective probabilities are very similar. As vaccine coverage increases, the probability of an outbreak reaching 50 infections drops below the probability of reaching 5 infections.

This shows that, in a highly vaccinated population, outbreaks may cause a few cases but increasingly fail to establish. These scenarios assume effective contact tracing is implemented once an outbreak is detected (either via a positive test result in the traveller who triggered the outbreak or via symptomatic community testing), so while vaccination levels are low, additional controls would almost always be necessary to control an outbreak. These results can also be interpreted in terms of the number of infected travellers that are expected to lead to one large outbreak (Table 8 , model output 3). Aside from those involving MIQ, the only scenario that consistently tolerates more than 80 infected travellers per large outbreak is 5-day selfisolation with daily LFTs and at least 80% domestic vaccine coverage, or 5-day self-isolation with two PCR tests and 90% vaccine coverage. Aside from MIQ, there is no scenario where domestic vaccine coverage is below 80% of over 12-year-olds and more than 80 infected travellers can be allowed to enter without a large outbreak being expected.

Results for the model with individual heterogeneity in the probability of testing positive (Supplementary Tables 2 -4) show that this appears to be a relatively small part of the overall stochasticity of the simulation results. Including heterogeneity has very little effect on the average relative transmission potential, but slightly increases the risk of undetected onward transmission relative to the base model. This is because more infected individuals will be missed, even when tested on multiple occasions. Further modelling work and better data on test characteristics are needed to more completely understand the sensitivity of the results to heterogeneity, but it appears to have a relatively small effect on the outcomes considered here.

If individuals tend to test positive earlier in the course of their infection (shifting the curves in Figure   2 to the left by 2 days), this decreases all measures of risk (Supplementary Tables 5-7) , particularly for interventions involving daily LFT testing. Conversely, if the generation time and incubation period are shorter (mean 2.9 days and 4.4 days respectively), the relative transmission potential is higher (Supplementary Table 8 ). However, this is not a good basis for comparison with the default parameter values (see Table 1 ) because the baseline (unmitigated) transmission potential depends on generation time assumptions. The risk of onward transmission (Supplementary Tables 9-10 ) is a better basis for comparison and this is lower for the short generation time scenario. This is because most transmission J o u r n a l P r e -p r o o f occurs in the first few days following infection, so testing and a period of self-isolation after arrival are more effective at preventing contact with the community during the infectious period.

When the sensitivity of LFTs is assumed to be lower (see Table 1 ), strategies using LFTs still outperform the corresponding strategy using PCR tests at reducing the probability of onward transmission (Supplementary Tables S11-S12) . LFT-based strategies become slightly worse than the corresponding PCR strategy at preventing onward transmission that is never detected (Supplementary Tables S13).

However, the difference is small and could be offset by a PCR test at the end of the self-isolation period (as described above). Finally, we performed a sensitivity analysis where self-isolation only prevents 40% of transmission from pre-symptomatic or asymptomatic arrivals in the community during and 60% of transmission from symptomatic arrivals (Supplementary Tables S13-S15), as opposed to 60%

and 80% in the base scenarios). As expected, the risk metrics are higher under most interventions, particularly those involving a 5-day self-isolation period. However, the relative risk reductions of the different policies follow the same qualitative features described above.

We have modelled the effect of different border controls on the risk of international travellers infected with SARS-CoV-2 transmitting the virus and triggering community outbreaks. Potential border measures include a requirement for travellers to be vaccinated, different combinations of predeparture testing and post-arrival testing and quarantine. We investigated outcomes at different levels of vaccine coverage in the domestic population.

The aim of this study is not to identify an optimal set of border interventions at a given vaccination rate. Relaxing border restrictions will increase the risk of border-related community outbreaks, including the risk per infected traveller and potentially also the volume of travellers. However, the tolerance a government has for border-related outbreaks will vary depending on factors such as the domestic vaccination rate, prevalence of SARS-CoV-2, capacity of public health systems, and overall strategy for community outbreak management. Tolerance is likely to increase over time in countries, such as New Zealand, transitioning away from a strict elimination strategy towards managing ongoing community transmission of SARS-CoV-2. Conversely, the emergence of new variants of concern could prompt a reduction in risk tolerance and tightening of border restrictions. Our study provides a 

If vaccine coverage is sufficiently high, the majority of border-related outbreaks may be stamped out with targeted measures like intensive community testing and contact tracing [4] . However, this would likely require significantly higher capacity than has been used in previous outbreaks in New Zealand.

In addition, some outbreaks may require broader interventions or even localised lockdowns, particularly if they affected population groups with relative low vaccine coverage or high contact rates.

This suggests a staged approach to relaxing travel restrictions with a gradual as opposed to a sudden increase in travel volume, allowing case management and outbreak control systems to be tested.

The over-dispersed nature of SARS-CoV-2 transmission implies many infected people do not transmit the virus, or only infect one or two others, whereas a small minority of cases can infect a large number of other people. This means that, although the probability of an individual transmitting the virus may be low, the ones who do transmit can lead to outbreaks that grow faster than an average would suggest.

The assumed reduction in transmission from individuals in self-isolation at home does not capture any specific effects, such as the increased relative likelihood of transmission to household contacts.

Policies such as requiring all household contacts of self-isolating travellers to be vaccinated or mandating the collection of contact tracing information would further mitigate risk. However, the effectiveness of home isolation is largely untested in the New Zealand context. Analysis of contact tracing data from March 2021 suggested that the introduction of a self-isolation requirement for international arrivals reduced transmission by 35% [25] , although this estimate was based on a small dataset that may not be representative of future cohorts of travellers. Columns headings 0%, 70%, 80%, and 90% refer to the percentage of 12-to-64-year-olds that are vaccinated in the community; all scenarios (except 0% coverage) assume 90% of over 65-year-olds are fully vaccinated. Results are from 100,000 independent simulations representing 100,000 infected travellers. For scenarios in which less than 100 of the 100,000 simulations resulted in a large outbreak, the number of infected travellers per large outbreak is shown as >1000.

J o u r n a l P r e -p r o o f

Probability of an infected vaccinated traveller starting a large outbreak leading to at least 50 infections (model output 2.iv)

PCR on day -3 >1000 >1000 >1000 >1000

LFT on day -1 >1000 >1000 >1000 >1000

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The authors acknowledge the support of the New Zealand Ministry of Health in supplying information on vaccine allocation in support of this work. The authors are grateful to Samik Datta, Nigel French, Jemma Geoghegan, Michael Hale, Richard Jaine, Markus Luczak-Roesch, Mike Maze, Matt Parry,

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