Pandemic spread in communities via random graphs
<jats:title>Abstract</jats:title> <jats:p>Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameter...
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Format: | Article |
Language: | English |
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IOP Publishing
2022
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Online Access: | https://hdl.handle.net/1721.1/145802 |
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author | Minzer, Dor Oz, Yaron Safra, Muli Wainstain, Lior |
author2 | Massachusetts Institute of Technology. Department of Mathematics |
author_facet | Massachusetts Institute of Technology. Department of Mathematics Minzer, Dor Oz, Yaron Safra, Muli Wainstain, Lior |
author_sort | Minzer, Dor |
collection | MIT |
description | <jats:title>Abstract</jats:title>
<jats:p>Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline the contacts between individuals in distinct communities. Given these parameters, we determine whether there will be an outbreak and if yes, we calculate the size of the giant-connected-component of the graph, thereby, determining the fraction of the population of each type that would be infected before it ends. We show that the pandemic spread has a natural evolution direction given by the Perron–Frobenius eigenvector of a matrix whose entries encode the average number of individuals of one type expected to be infected by an individual of another type. The corresponding eigenvalue is the basic reproduction number of the pandemic. We perform numerical simulations that compare homogeneous and heterogeneous spread graphs and quantify the difference between them. We elaborate on the difference between herd immunity and the end of the pandemic and the effect of countermeasures on the fraction of infected population.</jats:p> |
first_indexed | 2024-09-23T15:08:32Z |
format | Article |
id | mit-1721.1/145802 |
institution | Massachusetts Institute of Technology |
language | English |
last_indexed | 2024-09-23T15:08:32Z |
publishDate | 2022 |
publisher | IOP Publishing |
record_format | dspace |
spelling | mit-1721.1/1458022022-10-13T03:08:34Z Pandemic spread in communities via random graphs Minzer, Dor Oz, Yaron Safra, Muli Wainstain, Lior Massachusetts Institute of Technology. Department of Mathematics <jats:title>Abstract</jats:title> <jats:p>Working in the multi-type Galton–Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline the contacts between individuals in distinct communities. Given these parameters, we determine whether there will be an outbreak and if yes, we calculate the size of the giant-connected-component of the graph, thereby, determining the fraction of the population of each type that would be infected before it ends. We show that the pandemic spread has a natural evolution direction given by the Perron–Frobenius eigenvector of a matrix whose entries encode the average number of individuals of one type expected to be infected by an individual of another type. The corresponding eigenvalue is the basic reproduction number of the pandemic. We perform numerical simulations that compare homogeneous and heterogeneous spread graphs and quantify the difference between them. We elaborate on the difference between herd immunity and the end of the pandemic and the effect of countermeasures on the fraction of infected population.</jats:p> 2022-10-12T16:54:26Z 2022-10-12T16:54:26Z 2021 2022-10-12T16:48:23Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145802 Minzer, Dor, Oz, Yaron, Safra, Muli and Wainstain, Lior. 2021. "Pandemic spread in communities via random graphs." Journal of Statistical Mechanics: Theory and Experiment, 2021 (11). en 10.1088/1742-5468/AC3415 Journal of Statistical Mechanics: Theory and Experiment Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf IOP Publishing IOP Publishing |
spellingShingle | Minzer, Dor Oz, Yaron Safra, Muli Wainstain, Lior Pandemic spread in communities via random graphs |
title | Pandemic spread in communities via random graphs |
title_full | Pandemic spread in communities via random graphs |
title_fullStr | Pandemic spread in communities via random graphs |
title_full_unstemmed | Pandemic spread in communities via random graphs |
title_short | Pandemic spread in communities via random graphs |
title_sort | pandemic spread in communities via random graphs |
url | https://hdl.handle.net/1721.1/145802 |
work_keys_str_mv | AT minzerdor pandemicspreadincommunitiesviarandomgraphs AT ozyaron pandemicspreadincommunitiesviarandomgraphs AT saframuli pandemicspreadincommunitiesviarandomgraphs AT wainstainlior pandemicspreadincommunitiesviarandomgraphs |