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. 2020 Feb 17;10:2746. doi: 10.1038/s41598-020-59576-1

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Sketch of the multilayer structure of our model. The two top layers are the transportation lines through which vehicles move. Individuals wait at each node generating a queue q until a vehicle arrives and they are able to board if the vehicle is below full capacity c. Below the transportation lines, in gray, a the walking layer with infinite capacity connected to the transportation lines layer through inter-layer links.