<?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>S0120-419X2018000100021</article-id>
<article-id pub-id-type="doi">10.18273/revint.v36n1-2018002</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Different types of backward bifurcations on account of an improvement in treatment efficiency]]></article-title>
<article-title xml:lang="es"><![CDATA[Diferentes tipos de bifurcación hacia atrás a causa de una mejora en la eficiencia del tratamiento]]></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>21</fpage>
<lpage>35</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2018000100021&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2018000100021&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2018000100021&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  Understanding why there are multiple equilibrium points when R 0 &lt; 1 has been one of the main motivations to analyze existence of a backward bifurcation in epidemiological models. Existence of multiple endemic states is usually associated to branches of equilibrium points of the models, which could arise from either the disease-free equilibrium point if R 0 = 1 or from an endemic equilibrium point if R 0 &gt; 1. In this work, an SIR model with a density-dependent treatment rate is analyzed. The nature of the point where backward bifurcation emerges is explained in function of the velocity of the per-capita treatment rate. Strategies for the control or eradication of the disease will be proposed in function of the efficiency of the treatment.  MSC2010: 34C23, 34C40, 34C55, 34C60, 92D30.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Comprender por qué existen estados endémicos múltiples cuando R 0 &lt; 1 ha sido una de las principales motivaciones para analizar la existencia de una bifurcación hacia atrás en modelos epidemiológicos. La existencia de estados endémicos múltiples está asociada usualmente a ramas de puntos de equilibrio del sistema, las cuales pueden surgir ya sea desde el equilibrio libre de enfermedad si R 0 = 1, o desde un equilibrio no trivial si R 0 &gt; 1. En este trabajo se analiza un modelo del tipo SIR con una tasa de tratamiento densodependiente. Se explica la naturaleza del punto de donde surge la bifurcación hacia atrás en función de la velocidad de la tasa de tratamiento per cápita. Se propondrán estrategias para el control o erradicación de la enfermedad en función de la eficiencia del tratamiento.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Backward bifurcation]]></kwd>
<kwd lng="en"><![CDATA[forward bifurcation]]></kwd>
<kwd lng="en"><![CDATA[treatment]]></kwd>
<kwd lng="en"><![CDATA[SIR model]]></kwd>
<kwd lng="es"><![CDATA[Bifurcación hacia atrás]]></kwd>
<kwd lng="es"><![CDATA[bifurcación hacia adelante]]></kwd>
<kwd lng="es"><![CDATA[tratamiento]]></kwd>
<kwd lng="es"><![CDATA[modelo SIR]]></kwd>
</kwd-group>
</article-meta>
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