medRxiv preprint doi: https://doi.org/10.1101/2020.07.16.20155614; this version posted July 18, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license . based on data from July 1, 2020 Is it safe to lift COVID-19 travel bans? The Newfoundland story. Kevin Linka · Proton Rahman · Alain Goriely · Ellen Kuhl Received: July 17, 2020 Abstract A key strategy to prevent a local outbreak during position of having the coronavirus pandemic under control the COVID-19 pandemic is to restrict incoming travel. Once with the total number of 261 cases, with 258 recovered, a region has successfully contained the disease, it becomes 3 deaths, no active cases for 16 consecutive days, and no critical to decide when and how to reopen the borders. Here new cases for 36 days [1]. On the same day, after a two- we explore the impact of border reopening for the example months long local travel ban, the Atlantic Bubble opened to of Newfoundland and Labrador, a Canadian province that allow air travel between the four Atlantic Provinces, New- has enjoyed no new cases since late April, 2020. We com- foundland and Labrador, Nova Scotia, New Brunswick, and bine a network epidemiology model with machine learn- Prince Edward Island, with no quarantine requirements for ing to infer parameters and predict the COVID-19 dynam- travelers [34]. Under the increasing pressure to fully reopen, ics upon partial and total airport reopening, with perfect health officials and political decision makers now seek to un- and imperfect quarantine conditions. Our study suggests that derstand the risk of gradual and full reopening under perfect upon full reopening, every other day, a new COVID-19 case quarantine conditions and quarantine violation [23]. would enter the province. Under the current conditions, ban- The province of Newfoundland and Labrador is the ning air travel from outside Canada is more efficient in man- second smallest Canadian province with a population of aging the pandemic than fully reopening and quarantining 519,716. It has two major geographical divisions, the island 95% of the incoming population. Our study provides quan- of Newfoundland that accounts for 92% of the population titative insights of the efficacy of travel restrictions and can and a continental region of Labrador that is home to the re- inform political decision making in the controversy of re- maining 8% [33]. The demographics of its population, the opening. highest rates of obesity and overweight, metabolic disease, Keywords COVID-19 · epidemiology · SEIR model · and cancer nationally, and an unhealthy lifestyle with the reproduction number · machine learning highest rate of cigarette smoking among all provinces set Newfoundland and Labrador apart from the rest of Canada [2]. These factors are critical when developing policies for 1 Motivation the management of COVID-19. The first reported case of COVID-19 in Newfoundland On July 3, 2020, the Canadian province of Newfoundland and Labrador was on March 14, 2020 followed by a rapid es- and Labrador enjoyed the rather exceptional and enviable calation in the number of cases caused by a super-spreader event at a funeral home [34]. Rapid and well-coordinated Kevin Linka · Ellen Kuhl Department of Mechanical Engineering, Stanford University, Stanford, implementation of provincial public health measures re- California, United States E-mail: klinka/[email protected] sulted in excellent viral epidemic control of the first wave Proton Rahman and the province has not had a documented case of com- Department of Medicine Memorial University of Newfoundland, munity transmission since mid-April 2020 [1]. In the ab- Cananda E-mail: [email protected] sence of any reported COVID-19 cases in the province, the Alain Goriely risk of any future outbreaks will originate from travelers. Mathematical Institute, University of Oxford, Oxford, United King- On May 4, 2020 the Chief Medical Officer of the province dom E-mail: [email protected] issued a Special Measures Order stating that the only peo- NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. medRxiv preprint doi: https://doi.org/10.1101/2020.07.16.20155614; this version posted July 18, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license . 2 Kevin Linka et al. ple allowed to enter the province were residents of New- the infectious rate g. They are the inverses of the contact foundland and Labrador, asymptomatic workers, and those period B = 1=b, the latent period A = 1=a, and the infec- granted a permit due extenuating circumstances [29]. Since tious C = 1=g. For simplicity, we assume that the latency there is a limited number of entry points into Newfound- rate a = 1=2:5 days−1 and the infectious rate g = 6:5 days−1 land, with three quarters of all travelers entering via air [25], are disease-specific for COVID-19, and constant in space passenger air travel is a good metric to assess the impact and time [18, 19, 31]. To account for societal and political of travel restrictions on the importation risk in Newfound- actions [35], we introduce a behavior specific dynamic con- land [14]. tact rate b = b(t) that varies both in space and time. For A relaxation of the travel ban naturally induces anxiety easier interpretation, we express the contact rate, and fear of a new outbreak. From a public health perspective, the major challenges are (i) to understand the effect of the b(t) = R(t)g ; (2) travel bubble; (ii) to predict the effect of a wider opening to in terms of the dynamic effective reproduction number R(t) the rest of Canada and the United States; and (iii) to estimate [8], for which we make an ansatz of Gaussian random walk the effect of imperfect quarantine assuming that a fraction type [28] with a constant time-window of four days, of travelers would ignore the guidelines for self-isolation. Answering these questions will help to understand the short- R(t) = N(t; m;t): (3) and long-term effects of reopening. To explore whether and when it would be safe to lift Here N(t) is the time-varying Gaussian distribution, the travel ban, we model the dynamics of COVID-19 us- r t ing a network approach that links a local epidemiological N(t) = exp(−t(R(t) − m)2=2); (4) 2p model with air-traffic mobility [20]. Local epidemiological modeling [16] is now a well-accepted approach to follow parameterized in terms of the drift m and the daily stepwidth the dynamics of a homogeneous population during an epi- t = t∗=[1:0 − s], where t∗ is the the step width precision demic [12]. The extra network layers allow us to capture the and s is the associated smoothing parameter [22]. mobility between different local populations [21]. A unique feature of this approach is that we can dynamically infer the parameters of the epidemiology model using reported case 2.2 Mobility modeling data [17] and update it in real time during the progression of the disease [22]. In addition, we can easily extract mobility We model each province, territory, and state of North Amer- data from passenger air travel statistic between the differ- ica as a homogeneous population with its own local SEIR ent locations [14]. Here use this approch to study three re- dynamics and connect them to the province of Newfound- opening scenarios by gradually adding air traffic from (i) the land and Labrador through a global mobility network [3]. Atlantic Provinces; (ii) all of Canada; and (iii) all of North From this mobility network, we create a weighted graph G America. in which the i = 1;::;n nodes N represent the individual provinces, territories, and states and the weighted edges E represent the mobility between them [10]. We approximate 2 Methods the weights of the edges using the average daily passenger air travel statistics [14], and summarize this information in 2.1 Epidemiology modeling the adjacency matrix Aij that reflects the travel frequency be- tween two regions i and j, and in the degree matrix, We model the local epidemiology of the COVID-19 out- D = diag∑n A ; (5) break using an SEIR model [4,27] with four compartments, ii j=1;j6=i ij the susceptible, exposed, infectious, and recovered popula- that reflects the number of incoming passengers for each re- tions, governed by the set of ordinary differential equations, gion i. The difference between the degree matrix Dij and the adjacency matrix Aij defines the weighted graph Lapla- S˙ = −b(t)SI=N cian [20], E˙ = +b(t)SI=N − a E ˙ (1) I = + a E − g I Lij = Dij − Aij : (6) R˙ = + g I : For the province of Newfoundland and Labrador, the incom- Here (◦˙) = d(◦)=dt denotes the time-derivative of the com- ing and outgoing passenger air travel from and to other re- partment (◦˙) and N = S + E + I + R is the total population. gions is relatively similar and we can simply average the Three parameters govern the transition from one compart- two which results in an undirected graph G and symmetric ment to the next: the contact rate b, the latency rate a, and adjacency and Laplacian matrices, Aij = Aji and Lij = Lji.