Heterogeneous impact of a lockdown on inter-municipality mobility

Open Access

Heterogeneous impact of a lockdown on inter-municipality mobility

Hygor P. M. Melo, João Henriques, Raquel Carvalho, Trivik Verma, João P. da Cruz, and N. A. M. Araújo

Phys. Rev. Research 3, 013032 – Published 13 January 2021

Abstract

Without a vaccine, the fight against the spreading of the coronavirus has focused on maintaining physical distance. To study the impact of such measures on inter-municipality traffic, we analyze a mobile dataset with the daily flow of people in Portugal in March and April 2020. We find that the reduction in inter-municipality traffic depends strongly on its initial outflow. In municipalities where the mobility is low, the outflow reduced by $10 - 20 %$ and this decrease was independent of the population size. Whereas, for municipalities of high mobility, the reduction was a monotonic increasing function of the population size and it even exceeded $60 %$ for the largest municipalities. As a consequence of such heterogeneities, there were significant structural changes on the most probable paths for the spreading of the virus, which must be considered when modeling the impact of control measures.

Received 28 June 2020
Accepted 20 December 2020

DOI:https://doi.org/10.1103/PhysRevResearch.3.013032

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Epidemic Spreading

Transportation networks

Epidemic spreading

Statistical Physics & ThermodynamicsNetworks

Authors & Affiliations

Hygor P. M. Melo ^1,*, João Henriques^2,3, Raquel Carvalho², Trivik Verma ⁴, João P. da Cruz ^1,5,6,7, and N. A. M. Araújo ^1,6,†

¹Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, 1749–016 Lisboa, Portugal
²NOS, SGPS, S.A., 1600–404 Lisboa, Portugal
³Altran Portugal, 1990–096 Lisboa, Portugal
⁴Faculty of Technology, Policy and Management, Delft University of Technology, 2628BX Delft, The Netherlands
⁵Closer Consultoria, 1070–101 Lisboa, Portugal
⁶Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749–016 Lisboa, Portugal
⁷School for Data Science and Computational Thinking, Stellenbosch Un. 44 Banghoek Road, Stellenbosch, 7602, South Africa

^*hpmelo@fc.ul.pt
^†nmaraujo@fc.ul.pt

Article Text

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Supplemental Material

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References

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Issue

Vol. 3, Iss. 1 — January - March 2021

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Images

Figure 1
Effect of the lockdown in the mobility pattern of residents and nonresidents in Portugal. The relative mobility is calculated as the total number of people that moved between two different municipalities on that day divided by the average between March 2 and 6 (see Sec. 4 for further details). The first control measures were announced in March 12, and the state of emergency was declared on March 18. We see that during the lockdown the mobility of residents and nonresidents decreased to about 20% and 45% of the baseline. The maps show the spatial distribution of the relative mobility for three specific days (March 9, March 19, and April 23), for residents (R1, R2, and R3) and for nonresidents (N1, N2, and N3).
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Figure 2
Shortest-path trees and effective distances before the lockdown. Shortest-path trees from (a) Lisbon, (b) Braga, and (c) Campo Maior (central nodes). Each node is a different municipality and the distance to the central node is proportional the effective distance $D_{eff}$ , as defined in Sec. 4. The effective distances are calculated from the origin-destination matrix of the average mobility between March 2 and 6. The nodes are colored according to the geographical distance to the central node. In the bottom row are the country maps, where the color of each municipality is given by the effective distance from the corresponding central municipality marked by a black circle.
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Figure 3
The effect of the lockdown on the mobility network. (a) Shortest-path tree from Lisbon for three different days. The position of the nodes is given by the Fain Hu layout [30], designed to distribute symmetrically the nodes and minimize edge crossing. The color of each node is given by the effective distance from Lisbon. (b) Time dependence of the average effective distance in the shortest-path trees shown in Fig. 2. Before the lockdown, for these three municipalities, Lisbon had the shortest average distance to the rest of the country, followed by Braga and Campo Maior. With control measurements, the three average effective distances increased, reaching a maximum in the Easter holidays, when the Portuguese government imposed more severe mobility restrictions to inter-municipality travels. (c) Spearman's correlation coefficient $r$ between the effective distance from the average origin-destination matrix from March 2 to 6, and all the days of March and April. With the lockdown, the rank of the effective distances have changed as shown. (d) Time evolution of the node degree $k$ (number of edges) for Lisbon, Braga, and Campo Maior, for the shortest-path trees shown in Fig. 2. Initially, Lisbon was connected directly to more than 90% of the municipalities. With the lockdown, the $k$ decreases reaching a minimum at the Easter holidays, with only less than 50% of the municipalities connected with Lisbon by only one edge.
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Figure 4
The impact of the lockdown depends on the mobility pattern of the municipality. Outflow of each municipality before and during the lockdown. To reduce the statistical noise, the outflow corresponds to averages over five days: before any control measurements, we considered March 2 to 6, and for during the lockdown April 22 to 26. We show in the Supplemental Material [31] that a similar result is obtained when averaging over 10 days. Each colored circle is a municipality and the black solid line is a guide for the eyes and corresponds to a linear relation between the two. The color of each data point represents the population size of the municipality, following the log-spaced bins shown in the inset. We can see that the effect of the lockdown is not homogeneous across the country, municipalities with large values of mobility at the beginning of March showed a large reduction in April. In the inset is the relative change on outflow of each municipality (cyan circles) as a function of its population size. The relative change is calculated by the outflow difference between March and April divided by the one in March. The colors are given by the average relative change on outflow in log-spaced bins (based on the population size). The gray dashed line shows the average value of the relative outflow for the smaller municipalities ( $< 18 00$ people), and the dashed black line is the best fit for a logarithmic dependence of the relative outflow (RO) on the population size ( $P$ ) for large municipalities ( $> 18 000$ people) $RO = 0.27 {log}_{10} (P) - 1.02$ , while for smaller municipalities the best fit is $RO = - 0.06 {log}_{10} (P) + 0.33$ . The population for each municipality was obtained from Ref. [32].
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