key: cord-1039344-zgcvtvt1
authors: Hurford, A.; Rahman, P.; Loredo-Osti, J. C.
title: Modelling the impact of travel restrictions on COVID-19 cases in Newfoundland and Labrador
date: 2020-09-03
journal: nan
DOI: 10.1101/2020.09.02.20186874
sha: 03706c8c363d9a1885deda1355c2874858dba87c
doc_id: 1039344
cord_uid: zgcvtvt1

BACKGROUND: In many jurisdictions public health authorities have implemented travel restrictions to reduce coronavirus disease 2019 (COVID-19) spread. Previous research has considered the impact of international travel restrictions on COVID-19 dynamics, but in response to the pandemic, policies that restrict travel within countries have also been implemented, and the impact of these restrictions is less well studied. On May 4th, 2020, Newfoundland and Labrador (NL) implemented travel restrictions such that non-residents were required to have exemptions to enter the province. METHODS: We fit a stochastic epidemic model to data describing the number of active COVID-19 cases in NL from March 14th - May 4th. We then predicted possible outbreaks over the 9 weeks subsequent to May 4th, with and without the travel restrictions, and for physical distancing scenarios ranging from a 40% to 70% reduction in the daily contact rate relative to pre-pandemic levels. RESULTS: We find that the mean number of clinical COVID-19 cases would have been 12.4 times higher without the travel restrictions. Furthermore, without the travel restrictions there is a substantial risk of very large outbreaks. INTERPRETATION: Using epidemic modelling, we show how the NL COVID-19 outbreak could have unfolded had the travel restrictions not been implemented. Both physical distancing and travel restrictions affect the local dynamics of the epidemic. Our modelling shows that the travel restrictions are a plausible reason why there were so few reported COVID-19 cases in NL in the 9 weeks after May 4th.

In response to the COVID-19 pandemic, travel restrictions have frequently been implemented (Studdert, Hall, and Mello 2020) , yet the efficacy of these restrictions has not been established. Some previous studies consider the impact of international travel restrictions (Chinazzi et al. 2020; Wells et al. 2020 ), but there is a paucity of studies considering restricted travel within a nation (but see Linka et al. 2020; Arino et al. 2020 ) making the implementation of travel restrictions controversial for public health authorities (Studdert, Hall, and Mello 2020) . Furthermore, the impact of travel restrictions on reducing COVID-19 spread is interwoven with the impacts of other public health measures: for example, the spread of imported cases depends on compliance with self-isolation directives for travellers, local physical distancing, and mask wearing. Travel restrictions were implemented in Newfoundland and Labrador (NL) on May 4 th , 2020, such that only NL residents and exempted individuals were permitted to enter the province. We use a mathematical model to consider a "whatif" scenario: specifically, "what if there were no travel-restrictions?", and in doing so, we quantify the impact that the travel restrictions had on the subsequent COVID-19 outbreak in NL.

Mathematical models appropriate for large populations will poorly predict the epidemic dynamics of smaller populations, such as NL, since chance events may dramatically alter an epidemic trajectory when there are only a few cases to begin with (Keeling and Rohani 2008) . Further, imported infections due to the arrival of infected travellers will have a disproportionately large effect when the number of local cases is few, which is often the case for regions with small populations. Therefore, to appropriately characterize the impact of the travel restrictions on the COVID-19 outbreak in NL, we use a stochastic mathematical model appropriate for modelling infection dynamics in small populations (Keeling and Rohani 2008) , and where a similar modelling approach has been used in other jurisdictions Hellewell et al. 2020 ). Our analysis quantifies the impact of travel restrictions by considering a higher rate of imported infections when there are no travel restrictions, and we use the model to predict the range of possible outbreak sizes that could have occurred in NL in the 9 weeks subsequent to May 4 th .

Our model is based on Plank and colleagues (2020) , which is used to model COVID-19 dynamics in New Zealand. Our model describes the epidemiological dynamics of COVID-19 such that NL residents are either susceptible to, infected with, or recovered from COVID-19. Infected individuals are further divided into symptomatic and asymptomatic infections, and individuals with symptomatic infections may be in either the pre-clinical stage (infectious, prior to the onset of symptoms), or the clinical stage (infectious and symptomatic). The categorization of individuals into these infection classes is consistent with previous work (Hellewell et al. 2020; Davies et al. 2020) .

Our model assumes that COVID-19 infections may spread when an infectious person contacts a susceptible person. Contact rates when physical distancing is undertaken in response to the pandemic are expressed in relative terms, as percentage reductions in the contact rate relative to pre-pandemic levels. We assume that the pre-pandemic contact rate was equivalent to a basic reproduction number of R 0 =2.4, where the definition of R 0 for our model is explained in Table 1. Our model assumes that infected travelers that fail to self-isolate enter the population and may infect susceptible NL residents, and the rate of contact between residents and travellers is assumed to be the same as between residents.

For individuals that are infectious (those with asymptomatic, pre-clinical and clinical infections), the probability of infection given a contact depends on the number of days since the date of infection , and infectivity further depends on whether the infection is pre-clinical, clinical or asymptomatic (Davies et al. 2020) . Individuals with clinical infections are relatively less infectious because these individuals are symptomatic and are more likely to self-isolate. Similar to models developed by other researchers, our model is formulated as a continuous time branching process (Arino et al. 2020; Hellewell et al. 2020; Plank et al. 2020) . A branching process is a type of stochastic model where on any given simulation run, the predicted epidemic may be different since the epidemiological events, and the timing of these events, take values drawn from probability distributions. For example, our model assumes that the number of new infections generated by an infectious person follows a Poisson distribution with a mean that depends on physical distancing, the number of susceptible individuals in the population, the type of infection the infected individual has (asymptomatic, pre-clinical, or clinical) , and the number of days since the date of infection (see equation 1 in the Appendix). Most other aspects of our model, for example, the timing of new infections, are similarly stochastic, each described by probability distributions that have appropriate characteristics, and as fully described in the Appendix. An overview of the model and all parameter values are given in Figure 1 and Table 1. Our model does not consider age-structure or contact rates between individuals in the population that vary in space and time, due to, for example, attending school or work. This latter model limitation is discussed in the Interpretation section. The model does not explicitly consider hospitalizations or disease-induced mortality because given the short timeframe of our model predictions (9 weeks) the model would frequently predict fewer than one hospitalized individual. We intentionally limit the complexity of our model, since when additional parameters are added to a model the uncertainty in the model predictions builds up, potentially to the point where the model predictions may become useless (Saltelli et al. 2020 -Mind the hubris) . The model is implemented in R and the code is publically available at https://doi.org/10.6084/m9.figshare.12906710.v2.

We assumed that the rate that infected individuals enter NL after May 4 th and fail to self-isolate is Poisson-distributed with a mean equal to 3 (no travel restrictions) and 0.24 per month (with travel restrictions), and this assumed mean rate (with travel restrictions) yields model predictions compatible with the reported number of cases of COVID-19 in NL after May 4 th (see Figure 2 ). These parameter values assume that without travel restrictions, travel to NL would be 12.5 times greater. We assumed that infected travellers may be asymptomatic or pre-clinical, and the proportion of infections that are asymptomatic is assumed to be the same for both travellers and NL residents. The mean rate that infected travellers enter NL is assumed to be constant and the origin cities of the travellers is not considered.

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The copyright holder for this preprint this version posted September 3, 2020. . https://doi.org/10. 1101 /2020 Data describing the number of active COVID-19 cases is publically available and a copy of the data used for our analysis is archived with our code (Hurford, Rahman, and Loredo-Osti 2020) . We assumed that the contact rate between NL residents changed relative to its pre-pandemic level on March 18, 2020, when a public health emergency was declared in NL. We assumed that prior to March 18, 2020, the pre-pandemic basic reproduction number was R 0 =2.4, where the assumed value of R 0 affects how quickly the epidemic would grow with no public health measures in place. All model parameters, except the percentage reduction in the contact rate from March 19 th to May 4 th due to the declaration of the public health emergency, c 1 , were estimated independently of the NL COVID-19 case data. To fit c 1 given the data, we assumed that all clinical cases were reported, which is a reasonable assumption given the low number of cases reported in NL. We estimated c 1 = 30% by calibrating c 1 to the data describing the number of active COVID-19 cases in NL from March 19 th to May 4 th .

To determine the impact of travel restrictions, we characterize clinical infections occurring in NL after May 4 th as:

• Prior: the infected individual is part of an infection chain (i.e., a description of who infected whom) that originates from an NL resident infected prior to May 4 th . • Travel: the infected individual is a non-resident who was infected prior to travelling to NL.

• Local: the infected individual is an NL resident, who did not travel outside the province, and is part of an infection chain that originates from a traveller to NL.

The number of clinical cases that are 'travel-related' is calculated as the sum of infections characterized as 'travel' and 'local'. The model-predicted number of COVID-19 cases refers only to clinical infections, and does not include asymptomatic infections, which, on average, would increase the number of COVID-19 cases by 18%.

The model-predicted number of active clinical COVID-19 cases in NL from March 14 th to May 4 th ( Figure 2 , lines) broadly agrees with the data describing the number of active COVID-19 cases in NL over this same period ( Figure 2 , black dots). After May 4 th , when the travel restrictions were implemented in NL, the NL COVID-19 case data ( Figure 2a , black dots) agrees with the model predictions for physical distancing scenarios that reduce the contact rate between individuals by ≥ 60% of the pre-pandemic level (Figure 2a ; green -60%, blue -70%, and light pink -80% lines).

The mean number of cases over the 9 weeks subsequent to May 4 th is, on average, 12.4 times greater without the travel restrictions (Table 2) . For the different physical distancing scenarios considered, the mean number of cases over the 9 weeks ranged from 14-48 clinical cases (without the travel restrictions), as compared to 1-4 clinical cases (with the travel restrictions; Table 2 and Figure 3a ). In addition, without the travel restrictions, the number of clinical cases during the 9 weeks can be very large (Table 2 and Figure 3a ). Specifically, for physical distancing at 60% of its pre-pandemic level, the upper limit on the 95% confidence interval for the number of clinical cases over the 9 weeks is 79 (without the travel restrictions) and 17 (with the travel restrictions; Table 2, Figure 3a ).

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The impact of the travel restrictions is even more substantial when only travel-related cases are considered ( Figure 3b ) since almost all infections arising when the travel restrictions were implemented are attributed to infection chains that arise from a NL resident infected prior to May 4 th . The mean number of cases of each infection type: 'prior', 'travel' and 'local' are shown in Figure 4 .

Our model predictions broadly agree with the data describing the number of active COVID-19 cases in NL reported from March 14 th to May 4 th . Our modelling shows that failing to implement the travel restrictions on May 4 th would have resulted in 12.4 times more COVID-19 cases over the subsequent 9 weeks (Table 2) . Furthermore, without the travel restrictions, large outbreaks are much more likely (Table 2; Figure 3a ). Travel restrictions alone may be insufficient to limit COVID-19 spread since the level of physical distancing undertaken by the local community, which affects the contact rates between residents, is also a strong determinant of the outbreak size (Figures 2-4 ).

We found that the relative increase in the mean number of clinical infections without the travel restrictions (12.4 times larger; see Table 2 ) was nearly exactly equal to the relative increase in the importation rate without the travel restrictions (12.5 times larger; see Table 1 ). This equivalency was expected due to the hypothesized linear relationship between the importation rate and the mean outbreak size as noted in Anderson et al. 2020 . Specifically, if the mean outbreak size for one importation, I 1 , is equal for all importations, the total outbreak size arises by adding the outbreaks due to each importation, and is calculated as I tot =λ v I 1 , where λ v is the importation rate. A consequence of this linear relationship is that a relative increase in the importation rate due to lifting travel restrictions results in the same relative increase in the mean outbreak size. The assumptions and characteristics of our model that give rise to this linear relationship are discussed in Table 3 along with examples of conditions where these assumptions would be violated.

Related research, using North American airline passenger data from January 1, 2019 to March 31, 2020, in combination with epidemic forecasting, found that depending on the type of travel restrictions, the effective reproduction number, and the percentage of travellers quarantined, it would take between 37 and 128 days for 520 COVID-19 cases to accumulate in NL ( Table 2 in Linka et al. 2020 ). These predicted epidemic trajectories are consistent with our results, however, in contrast to Linka and colleagues who use a deterministic epidemic model (equation 7 in Linka et al. 2020 ), our epidemic model is stochastic and so outbreaks have an associated distribution of sizes ( Figure 3) .

Our model does not consider spatial structure such that individuals contact each other in schools, workplaces, or 'bubbles'. The absence of spatial structure in our model may over-estimate the probability of an epidemic establishing and the total number of cases until the outbreak subsides (Keeling 1999) . Related research, however, does consider spatially structured interactions in workplaces, businesses and schools, and concludes that without the travel restrictions implemented in NL on May 4 th the number COVID-19 cases would have been 5-20 times greater (Aleman 2020) . Travel restrictions are one of several approaches available to health authorities for COVID-19 management. Future research should consider the role travel restrictions, testing, contact tracing and physical distancing, as elements of comprehensive approach to the best management of COVID-19.

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With the travel restrictions in place, the model's predictions are consistent with data describing the number of active COVID-19 cases in NL reported from May 4 th -June 21 st . We assumed that without the travel restriction there would have been 12.5 times more imported COVID-19 cases, however, we were not able to estimate this value from data. Other research shows that without travel restrictions a new COVID-19 case would enter NL every other day (Linka et al. 2020 ). In addition, we were not able to estimate the percentage of travellers to NL that comply with self-isolation directives. Smith et al. (2020) found that 75% of survey participants reporting COVID-19 symptoms (high temperature and/or cough) also report having left their house in the last 24 hours, violating the lockdown measures in place in the UK at the time, and so non-compliance rates may be quite high.

At the time of the implementation of the travel restrictions, there were few COVID-19 infections in NL. Without the travel restrictions, most of the subsequent COVID-19 infections would have been initiated by infected travellers who failed to comply with self-isolation requirements and only the actions of NL residents (i.e., physical distancing), and local health authorities (i.e., testing and contact tracing) would be sufficient to slow the exponential growth of these infection chains in the local community.

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The copyright holder for this preprint this version posted September 3, 2020. Proportion of infections that are asymptomatic Known to take a wide range of values (Saltelli et al. 2020 ). Our estimate is . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 3, 2020. . https://doi.org/10.1101/2020.09.02.20186874 doi: medRxiv preprint consistent with Ng et al. 2020. η S = 0.25 Proportion reduction in infectivity for asymptomatic infections relative to clinical infections Davies et al. 2020 c iso = 0.5 Proportion reduction in infectivity for individuals with clinical infections due to self-isolation.

Davies et al. 2020

The pre-pandemic basic reproduction number. This is the number of secondary infections generated by an individual with a pre-clinical infection over their entire infectivity period, when all individuals in the population are susceptible. For our model, the definition of R 0 supposes that the level of infectivity corresponding to a pre-clinical infection is retained for the entire duration of the infectivity period (see equation 1 in the Appendix). Note that a percentage reduction in R 0 relative to its pre-pandemic level is equal to the same percentage reduction in the contact rate. Distribution of imported infections per month that fail to selfisolate when travel restrictions are in place after May 4 th . The mean value is 0.24 infected travellers per month that fail to self-isolate.

Fit to NL COVID-19 case data when c 2 ≥ 60% (see Figure 2 ) z 2~P OIS(0.1) Distribution of imported infections per month that fail to selfisolate when there are no travel restrictions after May 4 th . The mean value is 3 infected travellers per month that fail to self-isolate.

Mean is assumed to be 12.5 times greater than when travel restrictions are in place Table 2 . Model-predicted number of clinical COVID-19 cases in the 9 weeks subsequent to May 4 th with and without the implementation of travel restrictions.

Model-predicted clinical COVID-19 cases over 9 weeks . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 3, 2020. Table 3 . A list of the assumption and characteristics of our model that give rise to the linear relationship between the importation rate and the mean outbreak size. The linear relationship is that I tot =λ v I 1 , where I tot is the mean total number of cases, λ v is the importation rate, and I 1 is the mean number of cases that arise from one importation.

Effect of violating the assumption on outbreak size Mixing between individuals in the population is homogeneous.

Homogeneous mixing means than an infected person is equally likely to contact every susceptible person in the population.

A group of travellers, all of whom are infected, fail to selfisolate, but also travel everywhere together and contact all of the same people.

Mixing is non-homogeneous because group members are constrained to have contacts only amongst the same individuals as the other group members, and not all individuals in the population.

No matter what the size of the group, the resulting outbreak will be of similar size since the contacts of group members are redundant. Here, the mean outbreak size is not linearly related to the importation rate because a larger group would correspond to a larger number of importations, yet the resulting outbreak would not be much larger.

The susceptible population is Infected individuals that arrive later will . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 3, 2020. generate smaller infection chains due to fewer susceptible people to infect. Therefore, the total outbreak size cannot be calculated by summing the size of the outbreaks per importation, since the timing of the importation affects the outbreak size due to that importation. The number of people an infected person contacts is unchanged during the timeframe of interest.

Waning compliance with public health measures; school re-openings.

As above, outbreak sizes per importation cannot be added to determine the total outbreak size because the timing of the importations affects the value of the outbreak size per importation. Infectivity does not change over time.

See above.

Effect of considering the different characteristic Few 'prior' cases: cases that are not attributable to importations (see

High infection prevalence in absence of importations.

The relationship between travel-related cases and the importation rate will be linear, but total infections is the sum of prior cases and travel-related cases, such that the linear relationship will not hold. The quantity of interest is the mean outbreak size.

The quantity of interest is the median or the 2.5 th and 97.5 th quantiles to generate a 95% confidence interval.

The linear relationship with the importation rate applies only to the mean outbreak size. As can be observed in Table 2 , the linear relationship does not apply to the median or 95% confidence intervals. 

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The copyright holder for this preprint this version posted September 3, 2020. . https://doi.org/10.1101/2020.09.02.20186874 doi: medRxiv preprint cannot be re-infected. Infected travellers that fail to self-isolate enter the population at a mean rate, λ V (t). When a new infections occurs, a proportion, π, of these newly infected individuals are asymptomatic, where the number of individuals with asymptomatic infections at any time is A. Alternatively, a proportion, 1-π, of infected individuals will eventually develop clinical symptoms, although these individuals are initially pre-clinical (without symptoms), and the number of individuals that are pre-clinical at any time is P. At a mean rate, λ P (t), individuals with pre-clinical infections develop clinical infections (with symptoms). Individuals with asymptomatic, pre-clinical, and clinical infections are infectious (blue boxes), and infectivity depends on the type of infection, and the number of days since the date of infection. Finally, both individuals with asymptomatic and clinical infections recover at mean rates λ A (t) and λ C (t), respectively. See the Appendix for further details.

After May 4 th , we consider an alternative past scenario where no travel restrictions were implemented (b). Both with (a) and without (b) the travel restrictions, we consider different levels of physical distancing, represented as percentage reductions in the daily contact rate relative to pre-pandemic levels (coloured lines). Each coloured line is the mean number of active clinical cases each day calculated from 1000 runs of the stochastic model, which considers variability in the timing and changes in the number of individuals with different COVID-19 infection statuses.

health emergency declaration travel restrictions with travel restrictions . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 3, 2020 . . https://doi.org/10.1101 /2020 Figure 3. The total model-predicted number of COVID-19 cases in NL occurring over 9 weeks beginning on May 4 th when travel restrictions are implemented (yellow boxes) is much less than the total number of cases occurring over this same period if the travel restrictions were not implemented (green boxes). The total number of COVID-19 cases occurring during the 9 weeks subsequent to May 4 th is highly variable, and without the implementation of the travel restrictions there is a higher risk of a large outbreak (also see Table 2 ). When the travel restrictions are implemented, almost all of the cases occurring during the 9 weeks subsequent to May 4 th are due to infected individuals present in the community prior to May 4 th . Travel-related cases are all cases remaining after the 'prior' cases are removed (b). For each simulation, chance events affect the number of individuals that change COVID-19 infection statuses and the timing of these changes. The horizontal lines are medians, and the colored boxes and vertical lines capture 50% and 95% of the 1000 simulation outcomes, respectively, with outliers shown as dots. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 3, 2020 . . https://doi.org/10.1101 /2020 The source of infections is either: an individual infected prior to May 4 th ('prior', light blue); an individual that was infected prior to entering NL ('travel', green); or a NL resident that did not travel, but is part of an infection chain where the initial infectee is a traveller that entered NL after May 4 th ('local', mid-blue) . Our model assumptions are reflected by the difference in the number of COVID-19 cases occurring in travellers over the 9 weeks (green bars): approximately 1.5 with travel restrictions (a), as compared to 6.3 without travel restrictions (b). These infected travellers seed infection chains in the NL community resulting in a larger number of NL residents infected when the travel restrictions are not implemented (mid-blue bars). Both with and without the travel restrictions, the number of cases due to prior infection in the NL community is similar (light blue bars).

1. Infected individuals either: (i) will show clinical symptoms at some point during their infection (1-π)%), or (ii) will be asymptomatic (π%).

2. Individuals that are pre-clinical, clinical, or asymptomatic (see Figure 1 ) are all infectious with different levels of infectivity given a contact with a susceptible person. The infectivity of infected individuals changes depending on the number of days since infection onset and follows a Weibull distribution that is parameterized such that peak infectivity occurs . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted September 3, 2020. . https://doi.org/10.1101/2020.09.02.20186874 doi: medRxiv preprint approximately 5 days after the initial infection, and 90% of infections occur between 2.0 and 8.4 days after the infection onset. It is also assumed that 21 days after infection onset an individual is no longer infective. See for a justification of this assumption.

3. Individuals with asymptomatic infections are less likely to infect a susceptible person given a contact (relative to individuals with pre-clinical infections) where η S is a coefficient that scales the infectivity of asymptomatic individuals relative to pre-clinically infected individuals.

4. Clinically infected individuals are assumed to self-isolate, which reduces their infectivity by a factor c iso (relative to individuals with pre-clinical infections).

5. Infected individuals that will progress to have a clinical infection have an initial period when they are pre-clinical, T 1 . This distribution is the same as the distribution for the period from the date of infection to self-isolation, and is gamma-distributed, s ~ Γ(6.1,1.7). Note that we let s ≈ T 1 + T 2 , where T 1 and T 2 appear in Plank et al. 2020. 6 . Each infected individual j, per unit time, generates a Poisson-distributed number of new infections with a mean equal to λ j . This mean number of secondary infections depends on the fraction of susceptible people in the population, 1 -N(t)/N pop , the type of infection the infective person has, F j (t), the infectivity of the infected individual a given number of days since the date of infection, whether the infected person is in self-isolation, and the rate of contacts between individuals in the population.

The rate of infection for the j th individual (infected at the time t j ) on the time interval (t, t+Δt] is,

where,

(

f W (τ) is the density of the serial-interval time, W, and F j (t) and C(t) are given by, and,

where t 1 = March 18, 2020 is the date of the declaration of the health emergency in NL, and t 2 = May 4, 2020, the date of the implementation of the travel restrictions.

(3)

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The copyright holder for this preprint this version posted September 3, 2020. . https://doi.org/10.1101/2020.09.02.20186874 doi: medRxiv preprint 7. The time between an individual becoming infected and infecting another individual, the generation time, follows a Weibull distribution with a shape parameter equal to 2.83 and a scale parameter equal to 5.67 (mean value is 5 days). The infection times of all N j secondary infections from an individual j are independent identically distributed random variables from this distribution.

8. The number of infected travellers who fail to self-isolate on the time interval (t, t+Δt], V(t), follows a Poisson distribution with parameter λ V (t) given as, where r = restrictions corresponds to travel restrictions, and r = no restrictions corresponds to no travel restrictions.

The model is a stochastic birth-death process where births correspond to new infections and deaths correspond to the recovery of infected individuals. The counts arise from an inhomogeneous Poisson process, and the model describes a lagged process owing to the consideration of the serial interval distribution. The model is implemented in R using Euler's method (Gardner 2009 ).

Susceptible individuals become infected at a mean rate, λ S (t) = Σ j λ j (t) where λ j (t) is given by equation 1. Infected travellers that fail to self-isolate enter the population at a rate λ V (t) (equation 5). At a rate, λ P (t) = Σ j γ j P (t) individuals with pre-clinical infections develop clinical infections. Finally, both individuals with asymptomatic and clinical infections recover at rates λ A (t) = Σ j γ j A (t) and λ C (t) = Σ j γ j C (t), respectively. The probability of removing the j th individual from the K class in the time interval (t,t+Δt], given that this individual has not been removed before is, where f K (τ) and F K (τ) are the density and distribution functions for the time to removal from the K class.

An Agent-Based Approach to Model the Impact of Newfoundland and Labrador's Travel Ban on COVID Spread. Appendix B

How Much Leeway Is There to Relax COVID-19 Control Measures?

Assessing the Risk of COVID-19 Importation and the Effect of Quarantine

The Effect of Travel Restrictions on the Spread of the 2019 Novel Coronavirus (COVID-19) Outbreak

Effects of Non-Pharmaceutical Interventions on COVID-19 Cases, Deaths, and Demand for Hospital Services in the UK: A Modelling Study

Quantifying SARS-CoV-2 Transmission Suggests Epidemic Control with Digital Contact Tracing

Feasibility of Controlling COVID-19 Outbreaks by Isolation of Cases and Contacts

Modelling the Impact of Travel Restrictions on COVID-19 Cases in Newfoundland and Labrador

The Effects of Local Spatial Structure on Epidemiological Invasions

Stochastic Dynamics

Is It Safe to Lift COVID-19 Travel Bans? The Newfoundland Story

Projected Effects of Nonpharmaceutical Public Health Interventions to Prevent Resurgence of SARS-CoV-2 Transmission in Canada

A Stochastic Model for COVID-19 Spread and the Effects of Alert Level 4 in Aotearoa New Zealand

Five Ways to Ensure That Models Serve Society: A Manifesto

Statistics Canada

Partitioning the Curve -Interstate Travel Restrictions During the Covid-19 Pandemic

Quantifying SARS-CoV-2 Transmission Suggests Epidemic Control with Digital Contact Tracing

A Stochastic Model for COVID-19 Spread and the Effects of Alert Level 4 in Aotearoa New Zealand