key: cord-0957931-3zz2k6n1
authors: Kishore, N.; Kahn, R.; Martinez, P. P.; De Salazar, P. M.; Mahmud, A. S.; Buckee, C.
title: Lockdown related travel behavior undermines thecontainment of SARS-CoV-2
date: 2020-10-26
journal: nan
DOI: 10.1101/2020.10.22.20217752
sha: f27dee103ccade0fa2bf62f8abda3ff34253b89d
doc_id: 957931
cord_uid: 3zz2k6n1

In response to the SARS-CoV-2 pandemic, unprecedented policies of travel restrictions and stay-at-home orders were enacted around the world. Ultimately, the public's response to announcements of lockdowns - defined here as restrictions on both local movement or long distance travel - will determine how effective these kinds of interventions are. Here, we measure the impact of the announcement and implementation of lockdowns on human mobility patterns by analyzing aggregated mobility data from mobile phones. We find that following the announcement of lockdowns, both local and long distance movement increased. To examine how these behavioral responses to lockdown policies may contribute to epidemic spread, we developed a simple agent-based spatial model. We find that travel surges following announcements of lockdowns can increase seeding of the epidemic in rural areas, undermining the goal of the lockdown of preventing disease spread. Appropriate messaging surrounding the announcement of lockdowns and measures to decrease unnecessary travel are important for preventing these unintended consequences of lockdowns.

while in Spain we see an initial decrease in long distance travel with a much more severe decrease once all non-essential travel was restricted. It is important to note that even with lockdown measures, the baseline rate of local travel remains generally unchanged, at times including trips of 50 kilometers or more in both France and Spain. 67 To examine the epidemiological implications of these behavioral responses to lockdowns, we implemented a metapopulation 68 model reflecting the general behaviors we measured in the Facebook data. As shown in Figure 6 , which depicts results from an 69 epidemic without a lockdown or other interventions, we initiated the epidemic in an "urban" center (identified by a black outline) 70 with a higher population density and evaluated the epidemic spread across all other "non-urban" areas, with travel determined 71 by a gravity model of movement. We then varied travel and infection dynamics based on timing in relation to lockdown 72 announcements and implementations (Figure 7) . In the simulations, lockdowns affect behavior in two ways: first, between 73 announcement and lockdown implementation contact rates within populations (β 1 ) temporarily increase, and subsequently 74 decrease once the lockdown takes effect (β 2 ). Second, travel from urban to rural locations also changes prior to (α 1 ) and 75 following (α 2 ) lockdown. We evaluated each possible parameter combination against a relative baseline where this is no travel 76 surge and no increased contact rate during the period between lockdown announcement and implementation. an outbreak occurs, compared to the baseline scenario. This demonstrates the relative speed with which an epidemic is able to 88 seed surrounding communities. As contact rates and travel increase, there is a corresponding increase in seeding of epidemics 89 in new locations, as well as faster spread to all locations. This occurs because an increase in β 1 results in a larger number of 90 local cases available for travel while an increase in α 1 results in an increased overall probability of those cases traveling. 91 We evaluated the probability of travel (α 0 ) under varying parameter values in the null model (i.e. no change in movement 92 due to lockdown) with the goal of simulating a depopulation of the location that served as the urban center that was similar to 93 what we found empirically in Figure 2 . Across a variety of scenarios, an α 0 of 0.01 (baseline daily travel probability) resulted 94 in an at least 10% decrease in the population size of the urban center over the course of 60 days (Figures S1, S2 and S3). 96 Decreasing the time between announcement and lockdown implementation reduces the number of exported cases. As shown in 97 Figure 10 , an L 1 period of 0 days resulted in no discernible increase in risk of an epidemic across all locations compared to the 98 baseline. However, as we increased L 1 , the probability of having at least one case by thirty days increased in most non-urban 99 locations. This effect was especially notable in rural locations far removed from the urban center. Importantly, the speed of the 100 exportation of the epidemic was driven by both the duration of the L 1 period and modification of the travel surge as defined 101 by α 1 and β 1 . With an L 1 of 7 days, an α inc of three and a β inc of two, it is the locations that are closest to the urban center . CC-BY 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. (which was not certified by peer review)

The copyright holder for this preprint this version posted October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Discussion rates (β ) play a key role in the increased risk of exportation of cases to non-urban locations following announcement of a 109 lockdown. A temporary increase in local contact rates and mobility results in more epidemic seeding in rural areas compared to 110 if the lockdown were implemented without these increases ( Figure 8) . Importantly, α drives the speed of the epidemic and important tool for slowing the spread of an epidemic. However, the initial surges the lockdowns catalyze can cause the epidemic 148 to spread further and faster to places outside of urban centers that may be less equipped to deal with an epidemic. Travel surges thus necessitate increased surveillance, testing, and treatment in areas that historically are understaffed and under resourced.

Through the course of a partially controlled epidemic in a susceptible population, our simulation shows that rural areas will 151 still be affected, albeit at a later date ( Figure 12 ). Appropriate messaging to decrease the spike in local contact rates and exodus 152 out of epidemic areas along with inter-region coordination of movement can help decrease the burden of disease experienced by 153 rural areas.

Many simplifying assumptions were made in the simulation model, including homogeneous mixing within locations on the 156 lattice, a gravity model for connectivity, and the inclusion of only one urban center. Additionally, we assumed transmission 157 dynamics were the same between symptomatic and asymptomatic individuals. Individuals in the I compartment are not able to 158 travel immediately upon entering the I compartment, which may underestimate the amount of travel that would occur prior to 159 symptom onset; however, given that those in A are able to travel, this likely will not impact the overall dynamics. We further 160 assumed that increases in movement observed in the data following lockdown announcements coincided with increased contact 161 rates, particularly in light of the anecdotal evidence of "panic buying". However, in future outbreaks, interventions such as 162 masks and social distancing, which were not consistently implemented in many places when lockdowns were first initiated, . CC-BY 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 October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Facebook data set for each region, and; 3) the boroughs are of a large enough spatial scale to allow Facebook to capture highly 192 granular movement and population data. City level analyses were restricted to the United States as Facebook initiated a city 193 specific data collection pipeline for select cities on February 27th, well before the implementation of lockdown measures.

Country level analyses were restricted to Spain, India, and France as all three countries quickly implemented strict lockdown 195 measures, and Facebook initiated data collection pipelines for the whole country before these measures were put into place.

To assess the impact of different lockdown implementations and travel restrictions, we developed a simple metapopulation 198 model, consisting of 100 communities, evenly spaced on a ten-by-ten lattice. One community in the center represents an 199 "urban" area with a higher population size and population density than the other 99 "non-urban" locations. We make the 

Following the time step specific movement through the disease generation process individuals in each community are given 210 a chance to travel. This travel is driven by three factors: 1) the probability that an individual travels out of a given community, 211 α 0 ; 2) the probability that an individual from community i travels to community j, given that they will travel out of community 212 i, p i j | α 0 and; 3) the disease status of the individual. All individuals that are in the S, E, A and R compartments are able to 213 travel. Here we assume that individuals who are symptomatic and infectious will self-isolate and not travel. We first calculate 214 the number of individuals that leave each compartment in each community, and then distribute them into the same compartment 215 in another community, depending on the probabilities described above. As seen in Figure 2 where M i j is the i specific normalized value of a simple gravity model defined as:

Here the values for row and col return the row and column number of the community in our ten-by-ten lattice. Given that an 221 individual moves, the location that they move to is determined by a gravity model with locations that are closer and locations 222 which are more heavily populated (i.e. the urban center) receiving a higher probability of travel.

Timing and tuned parameters 224 We designed our model to describe three distinct periods of time: 1) L 0 , the period before any lockdown measures are announced 225 or implemented, 2) L 1 , the period of time after announcement of lockdown, but before implementation; and, 3) L 2 , the period of 226 time after the implementation of the lockdown (Figure 7) . As described above, the initial parameters of the disease generation 227 process and movement were controlled with α 0 and β 0 , which were tuned empirically. We varied six parameters which 228 influenced these initial parameters to evaluate the impact of differential implementation of lockdowns as shows in Figure 7 .

• α inc : A multiplicative factor which describes the increase in α 0 during the L 1 period resulting in α 1 . We used this variable 230 to simulate the increase in movement out of urban areas. α inc is assumed to be constant throughout the L 1 period.

• α dec : A multiplicative factor which describes the decrease in α 0 during the L 2 period resulting in α 2 . We used this 232 variable to simulate the reduction in movement between all locations resulting from the implementation of a lockdown. 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 October 26, 2020. ;

• β inc : A multiplicative factor which describes the increase in β 0 during the L 1 period resulting in β 1 . We used this variable 234 to increase the force of infection in areas where an epidemic had already started to simulate the increase in the contact 235 rate between individuals due to greater local movement.

• β dec : A multiplicative factor which describes the decrease in β 0 during the L 2 period resulting in β 2 . We used this 237 variable to decrease the force of infection in the areas where an epidemic had already started to simulate the decrease in 238 the contact rate likely after the implementation of lockdown measures.

• δ : The number of local symptomatic cases necessary for announcement and implementation of lockdown measures. 240 Here we assumed that all symptomatic cases were immediately identified.

• ω: The amount of time between announcement of a lockdown and implementation.

We simulated the stochastic epidemic 100 times. In each of the 100 communities, we calculated the proportion of simulations in 244 which that community had at least one case by day 30. We also calculated the average time to first infection across simulations 245 in each community. We compared these two metrics across variations of the six parameters described above. For our primary 246 analysis we held δ constant as it did not directly affect our question of interest. We subsequently varied δ to evaluate the 247 sensitivity of our model. . CC-BY 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.

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Number of communities 100 Size of urban center 4000 Size or "non-urban" areas 2500 Area of urban center 4 Area of "non-urban" areas 10 Number of initial infections 5 Latent period 5 days Infectious period 10 days Proportion symptomatic 0.5 α 0 (travel) 0.01 α inc 1, 1.5, 2, 2.5, 3 α dec 0.5, 1 β (force of infection) 0.0015 β inc 1, 1.5, 2 β dec 0.5, 1 ω (days between announcement and lockdown) 0, 3, 7 δ (cases to trigger lockdown) 10, 30 Time steps 60 days . CC-BY 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 October 26, 2020. ; Figure 1 . Percent change in population of Facebook users per region by day for boroughs in New York City, divided into times of day. The leftmost vertical black line is March 8th, 2020, the day that a number of schools began announcing closures. The rightmost vertical black line is the day that Governor Cuomo of New York ordered all New York City Schools closed.

. CC-BY 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 October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Figure 2 . Percent change in weekday nighttime population of Facebook users by city. We can see that all cities included in the Facebook sample experience a decrease in nighttime population over the period of interest.

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The copyright holder for this preprint this version posted October 26, 2020. ; Figure 3 . Percent change in population of Facebook users categorized by five equally sized quantiles of nightlight by country with data aggregated at the ADMIN3 level of spatial granularity.

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The copyright holder for this preprint this version posted October 26, 2020. ; Figure 4 . Percent change in population of Facebook users categorized by five equally sized quantiles of nightlight in Bangladesh with data aggregated at the ADMIN2 level of spatial granularity.

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The copyright holder for this preprint this version posted October 26, 2020. ; Figure 5 . Number of trips made by distance. Here we can see that in all three countries, long distance trips decreased significantly in the immediate aftermath of lockdown implementation. However, local travel, including trips that ranged from 50-200 km remained during lockdown. This data is not available for Bangladesh.

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The copyright holder for this preprint this version posted October 26, 2020. Figure 6 . Results of a simulation evaluating: probability of at least one case by 30 days (right) and the average day that the first case appeared (left). The location outlined in black is the "urban" center with a larger population size and density. All other locations are "non-urban" with the same population size and density. 

. CC-BY 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 October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Figure 8 . Average proportion of communities with an imported case. Initially the epidemic spread quicker in simulations with a large or small surge, however, simulations with no lockdown result in a larger overall epidemic size and eventually spread more rapidly.

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The copyright holder for this preprint this version posted October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint 

. CC-BY 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 October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Figure 11 . Overall epidemic size as over varying parameters. In all situations an epidemic with a lockdown (ie where there is a decrease in post lockdown travel) results in a smaller total epidemic size.

. CC-BY 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. (which was not certified by peer review)

The copyright holder for this preprint this version posted October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Figure 12 . Average time of first case. Communities that are further away from the urban center are generally seeded later.

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The copyright holder for this preprint this version posted October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Figure S1 . Depopulation of urban center with α 0 of 0.001.

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The copyright holder for this preprint this version posted October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Figure S2 . Depopulation of urban center with α 0 of 0.005.

. CC-BY 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. (which was not certified by peer review)

The copyright holder for this preprint this version posted October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint Figure S3 . Depopulation of urban center with α 0 of 0.01.

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The copyright holder for this preprint this version posted October 26, 2020. ; https://doi.org/10.1101/2020.10.22.20217752 doi: medRxiv preprint

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