Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation

In this paper, we develop a new node-based approximate model to describe contagion dynamics on networks. We prove that our approximate model is exact for Markovian SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical biology 2023-02, Vol.86 (2), p.22-22, Article 22
Main Authors: Hall, Cameron Luke, Siebert, Bram Alexander
Format: Article
Language:English
Subjects:
Applications of Mathematics
Approximation
Communicable Diseases - epidemiology
Differential equations
Disease Susceptibility
Exact solutions
Humans
Infections
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Nodes
Probability
Stochastic models
Trees
Upper bounds
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c355t-2e04109c55eabed0ca079822f5b20c094bc3cf398649e3da720ddff2d985dda3
container_end_page 22
container_issue 2
container_start_page 22
container_title Journal of mathematical biology
container_volume 86
creator Hall, Cameron Luke
Siebert, Bram Alexander
description In this paper, we develop a new node-based approximate model to describe contagion dynamics on networks. We prove that our approximate model is exact for Markovian SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source of infection, and that the model otherwise gives upper bounds on the probabilities of each node being susceptible. Our analysis of SEIR contagion dynamics is general to SEIR models with arbitrarily many classes of exposed/latent state. In all cases of a tree graph with a single source of infection, our approach yields a system of linear differential equations that exactly describes the evolution of node-state probabilities; we use this to state explicit closed-form solutions for an SIR model on a tree. For more general networks, our approach yields a cooperative system of differential equations that can be used to bound the true solution.
doi_str_mv 10.1007/s00285-022-01854-9
format article
fullrecord <record><control><sourceid>proquest_pubme</sourceid><recordid>TN_cdi_pubmedcentral_primary_oai_pubmedcentral_nih_gov_9832100</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2763333091</sourcerecordid><originalsourceid>FETCH-LOGICAL-c355t-2e04109c55eabed0ca079822f5b20c094bc3cf398649e3da720ddff2d985dda3</originalsourceid><addsrcrecordid>eNp9kUFv1DAQha2Kql0Kf4BDZYkLF8PYjpP4UglVW6hUCantEcly7MmSkrW3dgLl39fdLYVywBdbet-8mfEj5A2H9xyg-ZABRKsYCMGAt6pieo8seCUF4xWvX5AFSJCsbrk4JC9zvgHgjdL8gBzKuhZKN7AgX5d31k00x3GehhgytcHTLs7BZ9rHRANOP2P6Tq_OL7fS1bI81tHjmOmch7CilqYYJ_RsSojUbjYp3g1r--D2iuz3dsz4-vE-Itdny-vTz-ziy6fz048XzEmlJiYQKg7aKYW2Qw_OQqNbIXrVCXCgq85J10vd1pVG6W0jwPu-F163ynsrj8jJznYzd2v0DsOU7Gg2qYyRfploB_NcCcM3s4o_jG6lKD9ZDN49GqR4O2OezHrIDsfRBoxzNqKpZTmgeUHf_oPexDmFst2W4rXQbVUosaNcijkn7J-G4WAesjO77EzJzmyzM7oUHf-9xlPJ77AKIHdALlJYYfrT-z-292Gqpb0</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2763162984</pqid></control><display><type>article</type><title>Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation</title><source>Springer Nature</source><creator>Hall, Cameron Luke ; Siebert, Bram Alexander</creator><creatorcontrib>Hall, Cameron Luke ; Siebert, Bram Alexander</creatorcontrib><description>In this paper, we develop a new node-based approximate model to describe contagion dynamics on networks. We prove that our approximate model is exact for Markovian SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source of infection, and that the model otherwise gives upper bounds on the probabilities of each node being susceptible. Our analysis of SEIR contagion dynamics is general to SEIR models with arbitrarily many classes of exposed/latent state. In all cases of a tree graph with a single source of infection, our approach yields a system of linear differential equations that exactly describes the evolution of node-state probabilities; we use this to state explicit closed-form solutions for an SIR model on a tree. For more general networks, our approach yields a cooperative system of differential equations that can be used to bound the true solution.</description><identifier>ISSN: 0303-6812</identifier><identifier>EISSN: 1432-1416</identifier><identifier>DOI: 10.1007/s00285-022-01854-9</identifier><identifier>PMID: 36625970</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Approximation ; Communicable Diseases - epidemiology ; Differential equations ; Disease Susceptibility ; Exact solutions ; Humans ; Infections ; Mathematical and Computational Biology ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Nodes ; Probability ; Stochastic models ; Trees ; Upper bounds</subject><ispartof>Journal of mathematical biology, 2023-02, Vol.86 (2), p.22-22, Article 22</ispartof><rights>The Author(s) 2023</rights><rights>2022. The Author(s).</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>The Author(s) 2022</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c355t-2e04109c55eabed0ca079822f5b20c094bc3cf398649e3da720ddff2d985dda3</cites><orcidid>0000-0003-3370-6459</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/36625970$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Hall, Cameron Luke</creatorcontrib><creatorcontrib>Siebert, Bram Alexander</creatorcontrib><title>Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation</title><title>Journal of mathematical biology</title><addtitle>J. Math. Biol</addtitle><addtitle>J Math Biol</addtitle><description>In this paper, we develop a new node-based approximate model to describe contagion dynamics on networks. We prove that our approximate model is exact for Markovian SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source of infection, and that the model otherwise gives upper bounds on the probabilities of each node being susceptible. Our analysis of SEIR contagion dynamics is general to SEIR models with arbitrarily many classes of exposed/latent state. In all cases of a tree graph with a single source of infection, our approach yields a system of linear differential equations that exactly describes the evolution of node-state probabilities; we use this to state explicit closed-form solutions for an SIR model on a tree. For more general networks, our approach yields a cooperative system of differential equations that can be used to bound the true solution.</description><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Communicable Diseases - epidemiology</subject><subject>Differential equations</subject><subject>Disease Susceptibility</subject><subject>Exact solutions</subject><subject>Humans</subject><subject>Infections</subject><subject>Mathematical and Computational Biology</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nodes</subject><subject>Probability</subject><subject>Stochastic models</subject><subject>Trees</subject><subject>Upper bounds</subject><issn>0303-6812</issn><issn>1432-1416</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kUFv1DAQha2Kql0Kf4BDZYkLF8PYjpP4UglVW6hUCantEcly7MmSkrW3dgLl39fdLYVywBdbet-8mfEj5A2H9xyg-ZABRKsYCMGAt6pieo8seCUF4xWvX5AFSJCsbrk4JC9zvgHgjdL8gBzKuhZKN7AgX5d31k00x3GehhgytcHTLs7BZ9rHRANOP2P6Tq_OL7fS1bI81tHjmOmch7CilqYYJ_RsSojUbjYp3g1r--D2iuz3dsz4-vE-Itdny-vTz-ziy6fz048XzEmlJiYQKg7aKYW2Qw_OQqNbIXrVCXCgq85J10vd1pVG6W0jwPu-F163ynsrj8jJznYzd2v0DsOU7Gg2qYyRfploB_NcCcM3s4o_jG6lKD9ZDN49GqR4O2OezHrIDsfRBoxzNqKpZTmgeUHf_oPexDmFst2W4rXQbVUosaNcijkn7J-G4WAesjO77EzJzmyzM7oUHf-9xlPJ77AKIHdALlJYYfrT-z-292Gqpb0</recordid><startdate>20230201</startdate><enddate>20230201</enddate><creator>Hall, Cameron Luke</creator><creator>Siebert, Bram Alexander</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TK</scope><scope>7TM</scope><scope>7U9</scope><scope>7X7</scope><scope>7XB</scope><scope>88A</scope><scope>88E</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FI</scope><scope>8FJ</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FYUFA</scope><scope>GHDGH</scope><scope>GNUQQ</scope><scope>H94</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>K9.</scope><scope>L6V</scope><scope>LK8</scope><scope>M0S</scope><scope>M1P</scope><scope>M7N</scope><scope>M7P</scope><scope>M7S</scope><scope>M7Z</scope><scope>P5Z</scope><scope>P62</scope><scope>P64</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>7X8</scope><scope>5PM</scope><orcidid>https://orcid.org/0000-0003-3370-6459</orcidid></search><sort><creationdate>20230201</creationdate><title>Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation</title><author>Hall, Cameron Luke ; Siebert, Bram Alexander</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c355t-2e04109c55eabed0ca079822f5b20c094bc3cf398649e3da720ddff2d985dda3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Applications of Mathematics</topic><topic>Approximation</topic><topic>Communicable Diseases - epidemiology</topic><topic>Differential equations</topic><topic>Disease Susceptibility</topic><topic>Exact solutions</topic><topic>Humans</topic><topic>Infections</topic><topic>Mathematical and Computational Biology</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nodes</topic><topic>Probability</topic><topic>Stochastic models</topic><topic>Trees</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hall, Cameron Luke</creatorcontrib><creatorcontrib>Siebert, Bram Alexander</creatorcontrib><collection>SpringerOpen</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Neurosciences Abstracts</collection><collection>Nucleic Acids Abstracts</collection><collection>Virology and AIDS Abstracts</collection><collection>ProQuest Health &amp; Medical Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Medical Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>Hospital Premium Collection</collection><collection>Hospital Premium Collection (Alumni Edition)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>Health Research Premium Collection</collection><collection>Health Research Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>AIDS and Cancer Research Abstracts</collection><collection>SciTech Premium Collection (Proquest) (PQ_SDU_P3)</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer science database</collection><collection>ProQuest Health &amp; Medical Complete (Alumni)</collection><collection>ProQuest Engineering Collection</collection><collection>Biological Sciences</collection><collection>Health &amp; Medical Collection (Alumni Edition)</collection><collection>PML(ProQuest Medical Library)</collection><collection>Algology Mycology and Protozoology Abstracts (Microbiology C)</collection><collection>ProQuest Biological Science Journals</collection><collection>Engineering Database</collection><collection>Biochemistry Abstracts 1</collection><collection>ProQuest advanced technologies &amp; aerospace journals</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Biotechnology and BioEngineering Abstracts</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Journal of mathematical biology</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hall, Cameron Luke</au><au>Siebert, Bram Alexander</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation</atitle><jtitle>Journal of mathematical biology</jtitle><stitle>J. Math. Biol</stitle><addtitle>J Math Biol</addtitle><date>2023-02-01</date><risdate>2023</risdate><volume>86</volume><issue>2</issue><spage>22</spage><epage>22</epage><pages>22-22</pages><artnum>22</artnum><issn>0303-6812</issn><eissn>1432-1416</eissn><abstract>In this paper, we develop a new node-based approximate model to describe contagion dynamics on networks. We prove that our approximate model is exact for Markovian SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source of infection, and that the model otherwise gives upper bounds on the probabilities of each node being susceptible. Our analysis of SEIR contagion dynamics is general to SEIR models with arbitrarily many classes of exposed/latent state. In all cases of a tree graph with a single source of infection, our approach yields a system of linear differential equations that exactly describes the evolution of node-state probabilities; we use this to state explicit closed-form solutions for an SIR model on a tree. For more general networks, our approach yields a cooperative system of differential equations that can be used to bound the true solution.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><pmid>36625970</pmid><doi>10.1007/s00285-022-01854-9</doi><tpages>1</tpages><orcidid>https://orcid.org/0000-0003-3370-6459</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0303-6812
ispartof Journal of mathematical biology, 2023-02, Vol.86 (2), p.22-22, Article 22
issn 0303-6812
1432-1416
language eng
recordid cdi_pubmedcentral_primary_oai_pubmedcentral_nih_gov_9832100
source Springer Nature
subjects Applications of Mathematics
Approximation
Communicable Diseases - epidemiology
Differential equations
Disease Susceptibility
Exact solutions
Humans
Infections
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Nodes
Probability
Stochastic models
Trees
Upper bounds
title Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-02T20%3A03%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pubme&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Exact%20solutions%20and%20bounds%20for%20network%20SIR%20and%20SEIR%20models%20using%20a%20rooted-tree%20approximation&rft.jtitle=Journal%20of%20mathematical%20biology&rft.au=Hall,%20Cameron%20Luke&rft.date=2023-02-01&rft.volume=86&rft.issue=2&rft.spage=22&rft.epage=22&rft.pages=22-22&rft.artnum=22&rft.issn=0303-6812&rft.eissn=1432-1416&rft_id=info:doi/10.1007/s00285-022-01854-9&rft_dat=%3Cproquest_pubme%3E2763333091%3C/proquest_pubme%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c355t-2e04109c55eabed0ca079822f5b20c094bc3cf398649e3da720ddff2d985dda3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2763162984&rft_id=info:pmid/36625970&rfr_iscdi=true