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Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

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Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

Auteurs : Young-Ah Rho [États-Unis] ; Larry S. Liebovitch [États-Unis] ; Ira B. Schwartz [États-Unis]

Source :

Physics Letters. a [ 0375-9601 ] ; 2008.

RBID : PMC:7126121

Abstract

The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends on the disease parameters, the geometry of the migrations between the patches, and the addition of infected people into a patch. We found that there are significantly longer lived transients and additional “ancillary” epidemics when the reproductive rate R is closer to 1, as would be typical of SARS (Severe Acute Respiratory Syndrome) and bird flu, than when R is closer to 10, as would be typical of measles. In addition we show, both analytical and numerical, how the time delay between the injection of infected people into a patch and the corresponding initial epidemic that it produces depends on R.

Url:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7126121

DOI: 10.1016/j.physleta.2008.05.065
PubMed: NONE
PubMed Central: 7126121

Affiliations:

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PMC:7126121

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<front><div type="abstract" xml:lang="en"><p>The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends on the disease parameters, the geometry of the migrations between the patches, and the addition of infected people into a patch. We found that there are significantly longer lived transients and additional “ancillary” epidemics when the reproductive rate <italic>R</italic>
 is closer to 1, as would be typical of SARS (Severe Acute Respiratory Syndrome) and bird flu, than when <italic>R</italic>
 is closer to 10, as would be typical of measles. In addition we show, both analytical and numerical, how the time delay between the injection of infected people into a patch and the corresponding initial epidemic that it produces depends on <italic>R</italic>
.</p>
</div>
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<author><name sortKey="Banks, J E" uniqKey="Banks J">J.E. Banks</name>
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<pmc article-type="brief-report"><pmc-dir>properties open_access</pmc-dir>
  <front><journal-meta><journal-id journal-id-type="nlm-ta">Phys Lett A</journal-id>
<journal-id journal-id-type="iso-abbrev">Phys Lett A</journal-id>
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<article-categories><subj-group subj-group-type="heading"><subject>Article</subject>
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<title-group><article-title>Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events</article-title>
</title-group>
<contrib-group><contrib contrib-type="author"><name><surname>Rho</surname>
<given-names>Young-Ah</given-names>
</name>
<email>rho@ccs.fau.edu</email>
<xref rid="aff001" ref-type="aff">a</xref>
<xref rid="cor001" ref-type="corresp">⁎</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Liebovitch</surname>
<given-names>Larry S.</given-names>
</name>
<xref rid="aff001" ref-type="aff">a</xref>
<xref rid="aff002" ref-type="aff">b</xref>
</contrib>
<contrib contrib-type="author"><name><surname>Schwartz</surname>
<given-names>Ira B.</given-names>
</name>
<xref rid="aff003" ref-type="aff">c</xref>
</contrib>
</contrib-group>
<aff id="aff001"><label>a</label>
Florida Atlantic University, Center for Complex Systems and Brain Sciences, Boca Raton, FL 33431, USA</aff>
<aff id="aff002"><label>b</label>
Florida Atlantic University, Center for Molecular Biology and Biotechnology, Department of Psychology, Department of Biomedical Sciences, Boca Raton, FL 33431, USA</aff>
<aff id="aff003"><label>c</label>
Naval Research Laboratory, Code 6792, Plasma Physics Division, Washington, DC 20375, USA</aff>
<author-notes><corresp id="cor001"><label>⁎</label>
Corresponding author. <email>rho@ccs.fau.edu</email>
</corresp>
</author-notes>
<pub-date pub-type="pmc-release"><day>31</day>
<month>5</month>
<year>2008</year>
</pub-date>
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      <pub-date pub-type="ppub"><day>21</day>
<month>7</month>
<year>2008</year>
</pub-date>
<pub-date pub-type="epub"><day>31</day>
<month>5</month>
<year>2008</year>
</pub-date>
<volume>372</volume>
<issue>30</issue>
<fpage>5017</fpage>
<lpage>5025</lpage>
<history><date date-type="received"><day>26</day>
<month>10</month>
<year>2007</year>
</date>
<date date-type="rev-recd"><day>7</day>
<month>5</month>
<year>2008</year>
</date>
<date date-type="accepted"><day>14</day>
<month>5</month>
<year>2008</year>
</date>
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<permissions><copyright-statement>Copyright © 2008 Elsevier B.V. Published by Elsevier B.V. All rights reserved.</copyright-statement>
<copyright-year>2008</copyright-year>
<copyright-holder>Elsevier B.V.</copyright-holder>
<license><license-p>Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.</license-p>
</license>
</permissions>
<abstract><p>The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends on the disease parameters, the geometry of the migrations between the patches, and the addition of infected people into a patch. We found that there are significantly longer lived transients and additional “ancillary” epidemics when the reproductive rate <italic>R</italic>
 is closer to 1, as would be typical of SARS (Severe Acute Respiratory Syndrome) and bird flu, than when <italic>R</italic>
 is closer to 10, as would be typical of measles. In addition we show, both analytical and numerical, how the time delay between the injection of infected people into a patch and the corresponding initial epidemic that it produces depends on <italic>R</italic>
.</p>
</abstract>
<kwd-group><title>Keywords</title>
<kwd>Diseases</kwd>
<kwd>Epidemic models</kwd>
<kwd>Computer modeling and simulation</kwd>
<kwd>Ordinary differential equations</kwd>
<kwd>Flux based multi-patch models</kwd>
<kwd>Spatial heterogeneity</kwd>
<kwd>Annual driving</kwd>
<kwd>Transient time</kwd>
<kwd>Reproductive rate</kwd>
</kwd-group>
</article-meta>
<notes><p>Communicated by C.R. Doering</p>
</notes>
</front>
</pmc>
<affiliations><list><country><li>États-Unis</li>
</country>
<region><li>District de Columbia</li>
<li>Floride</li>
</region>
</list>
<tree><country name="États-Unis"><region name="Floride"><name sortKey="Rho, Young Ah" sort="Rho, Young Ah" uniqKey="Rho Y" first="Young-Ah" last="Rho">Young-Ah Rho</name>
</region>
<name sortKey="Liebovitch, Larry S" sort="Liebovitch, Larry S" uniqKey="Liebovitch L" first="Larry S." last="Liebovitch">Larry S. Liebovitch</name>
<name sortKey="Liebovitch, Larry S" sort="Liebovitch, Larry S" uniqKey="Liebovitch L" first="Larry S." last="Liebovitch">Larry S. Liebovitch</name>
<name sortKey="Schwartz, Ira B" sort="Schwartz, Ira B" uniqKey="Schwartz I" first="Ira B." last="Schwartz">Ira B. Schwartz</name>
</country>
</tree>
</affiliations>
</record>

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Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

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