{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T13:04:18Z","timestamp":1770469458517,"version":"3.49.0"},"reference-count":17,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["NHM"],"published-print":{"date-parts":[[2024]]},"abstract":"<abstract><p>Inspired by the COVID-19 pandemic, we build a large-scale epidemiological model that accounts for coordination between regions, each using travel restrictions in order to attempt to mitigate the spread of disease. There is currently a need for simulations of countries cooperating since travel restriction policies are typically taken without global considerations. It is possible, for instance, that a strategy which appears unfavorable to a region at some point during a pandemic might be best for containing the global spread, or that only by coordinating policies among several regions can a restriction strategy be truly effective. We use the formalism of hybrid automata to model the global disease spread among the coordinating regions. We model a connected network of coupled Susceptible-Exposed-Infected-Recovered (SEIR) models by considering a weighted directed graph with each node corresponding to a single region's disease model. The SEIR dynamics for each region admit terms for inter-regional travel determined by the graph's Laplacian that additionally accounts for travel restrictions between regions. The existence of an edge may change according to so-called guard conditions, which are triggered when the proportion of symptomatic infected individuals in a region reaches a critical value. Lastly, we run simulations in MATLAB of a global disease spreading among regions using automated travel restrictions and analyze the results.<\/p><\/abstract><\/jats:p>","DOI":"10.3934\/nhm.20240015","type":"journal-article","created":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T12:14:15Z","timestamp":1711714455000},"page":"324-354","source":"Crossref","is-referenced-by-count":1,"title":["Using hybrid automata to model mitigation of global disease spread via travel restriction"],"prefix":"10.3934","volume":"19","author":[{"given":"Richard","family":"Carney","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Monique","family":"Chyba","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taylor","family":"Klotz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.20240015-1","doi-asserted-by":"crossref","unstructured":"S. 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Ross, An application of the theory of probabilities to the study of a priori pathometry.\u2014Part I, Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character<\/i>, 92<\/b> (1916), 204\u2013230. https:\/\/doi.org\/10.1098\/rspa.1916.0007","DOI":"10.1098\/rspa.1916.0007"},{"key":"key-10.3934\/nhm.20240015-9","doi-asserted-by":"crossref","unstructured":"R. Ross, H. P. Hudson, An application of the theory of probabilities to the study of a priori pathometry.\u2014Part II, Proceedings of the Royal Society of London. Series A, Containing papers of a mathematical and physical character<\/i>, 93<\/b> (1917), 212\u2013225.","DOI":"10.1098\/rspa.1917.0014"},{"key":"key-10.3934\/nhm.20240015-10","doi-asserted-by":"publisher","unstructured":"R. Ross, H. P. Hudson, An application of the theory of probabilities to the study of a priori pathometry.\u2014Part III, Proceedings of the Royal Society of London. 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Tomlin, Hybrid systems: Foundations, advanced topics and applications<\/i>, Berlin: Springer Verlag, 2012."},{"key":"key-10.3934\/nhm.20240015-16","unstructured":"Port Authority Aviation Department, 2019 Annual Airport Traffic Report<\/i>, Port Authority of New York and New Jersey. Available from: https:\/\/www.panynj.gov\/content\/dam\/airports\/statistics\/statistics-general-info\/annual-atr\/ATR2019.pdf<\/ext-link>."},{"key":"key-10.3934\/nhm.20240015-17","unstructured":"T. Crowfoot, World population just passed 8 billion. Here's what it means, World Economic Forum. 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