<?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>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262012000100004</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Un modelo matemático sobre la dinámica del Mycobacterium tuberculosis en el granuloma]]></article-title>
<article-title xml:lang="en"><![CDATA[A Mathematical Model on Mycobacterium tuberculosis Dynamics into the Granuloma]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[IBARGÜEN-MONDRAGÓN]]></surname>
<given-names><![CDATA[EDUARDO]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[ESTEVA]]></surname>
<given-names><![CDATA[LOURDES]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de Nariño  ]]></institution>
<addr-line><![CDATA[Pasto ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Nacional Autónoma de México  ]]></institution>
<addr-line><![CDATA[México D. F ]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>15</day>
<month>06</month>
<year>2012</year>
</pub-date>
<pub-date pub-type="epub">
<day>15</day>
<month>06</month>
<year>2012</year>
</pub-date>
<volume>46</volume>
<numero>1</numero>
<fpage>39</fpage>
<lpage>65</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262012000100004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262012000100004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262012000100004&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[El propósito de este estudio es evaluar el impacto de la respuesta de las células T y los macrófagos en el control de Mtb dentro del granuloma. Con este fin, proponemos un sistema de ecuaciones diferenciales ordinarias para modelar la interacción entre macrófagos no infectados, macrófagos infectados, células T y bacilos de Mtb en el granuloma.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[The purpose of this study is to evaluate the impact of the response of T cells and macrophages in the control of Mtb into the granuloma. To this end, we propose a system of ordinary differential equations to model the interaction among uninfected macrophages, infected macrophages, T cells and Mtb bacilli into the granuloma.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Ecuaciones diferenciales ordinarias]]></kwd>
<kwd lng="es"><![CDATA[soluciones deequilibrio]]></kwd>
<kwd lng="es"><![CDATA[tuberculosis]]></kwd>
<kwd lng="es"><![CDATA[inmunología]]></kwd>
<kwd lng="en"><![CDATA[Ordinary Differential Equations]]></kwd>
<kwd lng="en"><![CDATA[Equilibrium Solutions]]></kwd>
<kwd lng="en"><![CDATA[Tuberculosis]]></kwd>
<kwd lng="en"><![CDATA[Immunology]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font size="2" face="verdana">      <p> <b> <font size="4">     <center> Un modelo matem&aacute;tico sobre la din&aacute;mica del <em>Mycobacterium tuberculosis</em> en el granuloma </center> </font> </b> </p>      <p> <b> <font size="3">     <center> A Mathematical Model on <em>Mycobacterium tuberculosis</em> Dynamics into the Granuloma </center> </font> </b> </p>      <p>     <center> EDUARDO IBARG&Uuml;EN-MONDRAG&Oacute;N<sup>1</sup>,  LOURDES ESTEVA<sup>2</sup> </center> </p>      <p> <sup>1</sup>Universidad de Nari&ntilde;o, Pasto, Colombia. Email: <a href="mailto:edbargun@udenar.edu.co">edbargun@udenar.edu.co</a>     <br>  <sup>2</sup>Universidad Nacional Aut&oacute;noma de M&eacute;xico, M&eacute;xico D. F, M&eacute;xico. Email: <a href="mailto:lesteva@lya.fciencias.unam.mx">lesteva@lya.fciencias.unam.mx</a>     <br> </p>  <hr size="1">      ]]></body>
<body><![CDATA[<p> <b>     <center> Resumen </center> </b> </p>      <p> El prop&oacute;sito de este estudio es evaluar el impacto de la respuesta de las c&eacute;lulas T y los macr&oacute;fagos en el control de Mtb dentro del granuloma. Con este fin, proponemos un sistema de ecuaciones diferenciales ordinarias para modelar la interacci&oacute;n entre macr&oacute;fagos no infectados, macr&oacute;fagos infectados, c&eacute;lulas T y bacilos de Mtb en el granuloma. </p>      <p> <b> Palabras clave: </b> Ecuaciones diferenciales ordinarias, soluciones deequilibrio, tuberculosis, inmunolog&iacute;a. </p>  <hr size="1">  <i>2000 Mathematics Subject Classification: 37C75, 92B05.</i>  <hr size="1">      <p> <b>     <center> Abstract </center> </b> </p>      <p> The purpose of this study is to evaluate the impact of the response of T cells and macrophages in the control of Mtb into the granuloma. To this end, we propose a system of ordinary differential equations to model the interaction among uninfected macrophages, infected macrophages, T cells and Mtb bacilli into the granuloma. </p>      <p> <b> Key words: </b> Ordinary Differential Equations, Equilibrium Solutions, Tuberculosis, Immunology. </p>  <hr size="1">      <p> Texto completo disponible en <a href="pdf/rcm/v46n1/v46n1a04.pdf">PDF</a> </p>  <hr size="1">      <p> <b> <font size="3"> Referencias </font> </b> </p>       ]]></body>
<body><![CDATA[<!-- ref --><p> &#91;1&#93; J. Alavez-Ram&iacute;rez, J. Avendano, L. Esteva, J. Flores, J. Fuentes- Allen, G. Garc&iacute;a-Ramos, G. Gom&eacute;z, and J. L. Estrada, 'Within-host population dynamics of antibiotic-resistant m. <em>tuberculosis</em>', <i>Math. Med. and Bio. J.</i> <i>24</i>, 1 (2007), 35-56.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000023&pid=S0034-7426201200010000400001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;2&#93; R. Antia, J. Koella, and V. Perrot, 'Model of the Within-Host Dynamics of Persistent Mycobacterial Infections', <i>Proc. R. Soc. Lond. B</i> <i>263</i>, 1 (1996), 257-263.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000025&pid=S0034-7426201200010000400002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;3&#93; J. Egen, A. Rothfuchs, C. Feng, N. Winter, A. Sher, and R. Germain, 'Macrophage and T Cell Dynamics During the Development and Disintegration of Mycobacterial Granulomas', <i>Immunity</i> <i>28</i>, 2 (2008), 271-284.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000027&pid=S0034-7426201200010000400003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;4&#93; F. Gantmacher, <i>The Theory of Matrices</i>, Chelsea House Publishers, London, United Kingdom,    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000029&pid=S0034-7426201200010000400004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 1960. </p>      <!-- ref --><p> &#91;5&#93; E. Ibarg&uuml;en-Mondrag&oacute;n, L. Esteva, and L. Ch&aacute;vez-Gal&aacute;n, 'A Mathematical Model for Cellular Immunology of Tuberculosis', <i>J. Mathematical Biosciences and Engineering</i> <i>8</i>, 4 (2011), 973-986.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000031&pid=S0034-7426201200010000400005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      ]]></body>
<body><![CDATA[<!-- ref --><p> &#91;6&#93; S. Kaufman, 'How Can Immunology Contribute to the Control of Tuberculosis', <i>Reviews J. Immunology</i> <i>1</i>, 1 (2001), 20-48.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000033&pid=S0034-7426201200010000400006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;7&#93; G. Magombedze, W. Garira, and E. Mwenje, 'Modelling the Human Immune Response Mechanisms to Mycobacterium Tuberculosis Infection in the Lungs', <i>J. Mathematical Biosciences and engineering</i> <i>3</i>, 4 (2006), 661-682.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000035&pid=S0034-7426201200010000400007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;8&#93; S. Marino and D. Kirschner, 'The Human Immune Response to the <em>Mycobacterium tuberculosis</em> in Lung and Lymphnode', <i>Journal of Theoretical Biology</i> <i>227</i>,  (2004), 463-486.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000037&pid=S0034-7426201200010000400008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;9&#93; Palomino, Le&aacute;o, and Ritacco, <i>Tuberculosis 2007, From Basic Science to Patient Care</i>, Tuberculosistextbook.com, Brasil,    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000039&pid=S0034-7426201200010000400009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> 2007. </p>      <!-- ref --><p> &#91;10&#93; D. Russell, 'Who Puts the Tubercle in Tuberculosis?', <i>Nature Rev Microbilogy</i> <i>jan</i>, 5 (2007), 39-47.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000041&pid=S0034-7426201200010000400010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      ]]></body>
<body><![CDATA[<!-- ref --><p> &#91;11&#93; M. Tsai, S. Chakravarty, G. Zhu, J. Xu, K. Tanaka, C. Koch, J. Tufariello, J. Flynn, and J. Chan, 'Characterization of the Tuberculous Granuloma in Murine and Human Lungs: Cellular Composition and Relative Tissue Oxygen Tension', <i>Cell Microbiol</i> <i>8</i>, 2 (2006), 218-232.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000043&pid=S0034-7426201200010000400011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>      <!-- ref --><p> &#91;12&#93; J. Wigginton and D. Kischner, 'A model to Predict Cell Mediated Imune Regulatory Mechanisms During Human Infection with <em>Mycobacterium tuberculosis</em>', <i>J. Immunology</i> <i>166</i>,  (2001), 1951-1967.    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000045&pid=S0034-7426201200010000400012&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> </p>  <hr size="1">      <center> <b>(Recibido en octubre de 2011. Aceptado en marzo de 2012)</b> </center> <hr size="1">      <p> Este art&iacute;culo se puede citar en <i>LaTeX</i> utilizando la siguiente referencia bibliogr&aacute;fica de <i>BibTeX</i>: </p> <code><font size="2" face="verdana"> @ARTICLE{RCMv46n1a04,    <br>   AUTHOR = {Ibarg&uuml;en-Mondrag&oacute;n, Eduardo and Esteva, Lourdes},    <br>   TITLE  = {{Un modelo matem&aacute;tico sobre la din&aacute;mica del \emph{Mycobacterium tuberculosis} en el granuloma}},    <br>   JOURNAL = {Revista Colombiana de Matem&aacute;ticas},    <br>  YEAR  = {2012},    ]]></body>
<body><![CDATA[<br>  volume = {46},    <br>  number = {1},    <br>  pages  = {39--65}    <br> } </font></code>  <hr size="1"> </font>      ]]></body><back>
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