<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2018000100037</article-id>
<article-id pub-id-type="doi">10.18273/revint.v36n1-2018003</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Existence of periodic solutions for seasonal epidemic models with quarantine]]></article-title>
<article-title xml:lang="en"><![CDATA[Existencia de soluciones periódicas para modelos epidemiológicos estacionales con cuarentena]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Guerrero-Flores]]></surname>
<given-names><![CDATA[Shaday]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Osuna]]></surname>
<given-names><![CDATA[Osvaldo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Villavicencio-Pulido]]></surname>
<given-names><![CDATA[Geiser]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Michoacana de San Nicolás de Hidalgo  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>México</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Michoacana de San Nicolás de Hidalgo  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>México</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Autónoma Metropolitana-Unidad Lerma  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>36</volume>
<numero>1</numero>
<fpage>37</fpage>
<lpage>47</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2018000100037&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2018000100037&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2018000100037&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  In this work, we establish the existence of periodic orbits for a seasonal saturated epidemiological model of a population consisting of susceptible, infectious and quarantined individuals (an SIQS model). To do so, we use Leray-Schauder degree theory. We also provide numerical examples of these solutions.  MSC2010: 37J45, 34C25, 92D30, 34D23.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  En este trabajo establecemos la existencia de órbitas periódicas para un modelo epidemiológico estacional con cuarentena y tasa de incidencia saturada. Para realizar lo anterior, usamos un esquema variacional basado en la teoría de grado de Leray-Schauder. También presentamos algunos ejemplos numéricos para ilustrar nuestros resultados analíticos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Leray-Schauder degree]]></kwd>
<kwd lng="en"><![CDATA[SIQS models]]></kwd>
<kwd lng="en"><![CDATA[periodic orbits]]></kwd>
<kwd lng="en"><![CDATA[reproductive number]]></kwd>
<kwd lng="es"><![CDATA[Grado de Leray-Schauder]]></kwd>
<kwd lng="es"><![CDATA[modelos SIQS]]></kwd>
<kwd lng="es"><![CDATA[órbitas periódicas]]></kwd>
<kwd lng="es"><![CDATA[número reproductivo básico]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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