<?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>0124-0064</journal-id>
<journal-title><![CDATA[Revista de Salud Pública]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. salud pública]]></abbrev-journal-title>
<issn>0124-0064</issn>
<publisher>
<publisher-name><![CDATA[Instituto de Salud Publica, Facultad de Medicina - Universidad Nacional de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0124-00642017000200194</article-id>
<article-id pub-id-type="doi">10.15446/rsap.v19n2.37634</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Ajuste de la fuerza de infección del dengue]]></article-title>
<article-title xml:lang="en"><![CDATA[Adjusted force of Dengue infection]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Aldana-Bermúdez]]></surname>
<given-names><![CDATA[Eliécer]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Restrepo-Triviño]]></surname>
<given-names><![CDATA[Maribel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Muñoz-Loaiza]]></surname>
<given-names><![CDATA[Aníbal]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Salamanca Departamento de Didáctica de la Matemática y Didáctica de las Ciencias Experimentales ]]></institution>
<addr-line><![CDATA[Salamanca ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad del Quindío Facultad de Educación ]]></institution>
<addr-line><![CDATA[Armenia ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad del Quindío Facultad de Ciencias Básicas y Tecnologías ]]></institution>
<addr-line><![CDATA[Armenia ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2017</year>
</pub-date>
<volume>19</volume>
<numero>2</numero>
<fpage>194</fpage>
<lpage>198</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0124-00642017000200194&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0124-00642017000200194&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0124-00642017000200194&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN  Objetivo  Plantear un modelo matemático hospedero vector para el ajuste de la fuerza de infección del dengue en una población variable con crecimiento logístico y ciclo de vida del mosquito con tasa de ovoposición periódica, considerando inmunidad a un serotipo.  Métodos  El modelo matemático propuesto está representado por ocho ecuaciones diferenciales a las que se les calcula la fuerza de infección por el método de las redes libres de escala.  Resultados  Se presenta una simulación del modelo matemático resuelto mediante un algoritmo implementado en el software MATLAB con datos obtenidos de la literatura. En la simulación se puede observar el crecimiento de la fuerza de infección del dengue a través del tiempo, donde esta varía de acuerdo al cambio de algunos parámetros.  Conclusiones  La fuerza de la infección aumenta en el tiempo, es decir, la tasa de nuevos casos crece, mostrando la necesidad de prevención en las personas, mediante el uso de telas metálicas, mosquiteros, repelentes, ropa adecuada entre otras medidas; control químico como larvicidas y adulticidas contra el vector, como también la eliminación de criaderos que interrumpan su ciclo de vida.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT  Objective  To propose a vector-host mathematical model for adjusting the force of infection with dengue in a variable population with logistic growth and a mosquito life cycle with periodic oviposition rate, considering immunity to a serotype.  Methods The proposed mathematical model is represented by eight differential equations that calculate the force of infection through the scale-free network method.  Results  A simulation of the mathematical model solved by an algorithm implemented in MATLAB based on data obtained from the literature was obtained. The growth of the force of dengue infection over time can be observed in the simulation, and it varies as some parameters change.  Conclusions  The force of infection increases over time, that is, the rate of new cases increases, which proves the need for prevention among inhabitants of high-risk areas through the use of metallic fabrics, mosquito nets, repellents, appropriate clothing, among other measures. Chemical control against the vector, such as larvicides and adulticides, as well as the elimination of breeding places to interrupt their life cycle are strongly advised.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Dengue]]></kwd>
<kwd lng="es"><![CDATA[modelo]]></kwd>
<kwd lng="es"><![CDATA[simulación]]></kwd>
<kwd lng="es"><![CDATA[fuerza]]></kwd>
<kwd lng="es"><![CDATA[infección]]></kwd>
<kwd lng="es"><![CDATA[(fuente: DeCS, BIREME).]]></kwd>
<kwd lng="en"><![CDATA[Dengue]]></kwd>
<kwd lng="en"><![CDATA[simulation]]></kwd>
<kwd lng="en"><![CDATA[model]]></kwd>
<kwd lng="en"><![CDATA[force]]></kwd>
<kwd lng="en"><![CDATA[infection]]></kwd>
<kwd lng="en"><![CDATA[(source: MeSH, NLM).]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bisset]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Blanco]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<name>
<surname><![CDATA[Braga]]></surname>
<given-names><![CDATA[I]]></given-names>
</name>
<name>
<surname><![CDATA[Coto]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
<name>
<surname><![CDATA[Massuh]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
<name>
<surname><![CDATA[Moncayo]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<name>
<surname><![CDATA[Nathan]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Orellano]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Vazquez Cangas]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Zerba]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Protocolo para determinar la susceptibilidad o resistencia a insecticidas de mosquitos de la especie Aedes aegypti, Documento propuesto por la Red Latinoamericana de Control de Vectores]]></source>
<year>2005</year>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clark]]></surname>
<given-names><![CDATA[G. G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Situación Epidemiológica del dengue en América. Desafíos para su Vigilancia y Control]]></article-title>
<source><![CDATA[Salud Publica México]]></source>
<year>1995</year>
<volume>37</volume>
<page-range>5-11</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Caetano]]></surname>
<given-names><![CDATA[MAL]]></given-names>
</name>
<name>
<surname><![CDATA[Yoneyama]]></surname>
<given-names><![CDATA[T]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal and sub-optimal control in dengue epidemics]]></article-title>
<source><![CDATA[Optimal control applications and methods]]></source>
<year>2001</year>
<volume>22</volume>
<page-range>63-73</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Busenberg]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<name>
<surname><![CDATA[Cooke]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<source><![CDATA[Vertically transmitted diseases]]></source>
<year>1988</year>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer - Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dye]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Models for the population dynamics of the yellow fever mosquito, Aedes aegypti]]></article-title>
<source><![CDATA[Journal of Animal Ecology]]></source>
<year>1984</year>
<volume>53</volume>
<page-range>247-68</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Espinoza]]></surname>
<given-names><![CDATA[FG]]></given-names>
</name>
</person-group>
<source><![CDATA[Dinámica de transmisión del dengue en la Ciudad de Colima, México]]></source>
<year>2002</year>
<publisher-name><![CDATA[Universidad de Colima]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Esteva]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Vargas]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A model for dengue disease with variable human population]]></article-title>
<source><![CDATA[Journal Mathematical Biology]]></source>
<year>1999</year>
<volume>38</volume>
<page-range>220</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mendes]]></surname>
<given-names><![CDATA[LP]]></given-names>
</name>
<name>
<surname><![CDATA[Codeco]]></surname>
<given-names><![CDATA[TC]]></given-names>
</name>
<name>
<surname><![CDATA[Massad]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
<name>
<surname><![CDATA[Struchiner]]></surname>
<given-names><![CDATA[CJ]]></given-names>
</name>
</person-group>
<source><![CDATA[Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil]]></source>
<year>2003</year>
<volume>98</volume>
<numero>7</numero>
<issue>7</issue>
<page-range>871-8</page-range><publisher-name><![CDATA[Memorias del Instituto Oswaldo Cruz]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Esteva]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Vargas]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Influence of vertical and mechanical transmission on the dynamics of dengue disease]]></article-title>
<source><![CDATA[Mathematical Biosciencie]]></source>
<year>2000</year>
<volume>167</volume>
<page-range>51-64</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Takahashi]]></surname>
<given-names><![CDATA[LT]]></given-names>
</name>
<name>
<surname><![CDATA[Maidana]]></surname>
<given-names><![CDATA[NA]]></given-names>
</name>
<name>
<surname><![CDATA[Ferreira]]></surname>
<given-names><![CDATA[JR]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[O Aedes e sua onda]]></article-title>
<source><![CDATA[Biomatemática]]></source>
<year>2003</year>
<volume>8</volume>
<page-range>33-44</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Esteva]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Vargas]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Coexistence of different serotypes of dengue virus]]></article-title>
<source><![CDATA[Journal Mathematical Biology]]></source>
<year>2003</year>
<volume>46</volume>
<page-range>31-47</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Feng]]></surname>
<given-names><![CDATA[Z]]></given-names>
</name>
<name>
<surname><![CDATA[Velasco Hernández J]]></surname>
<given-names><![CDATA[X]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Competitive exclusión in a vector host model for the dengue fever]]></article-title>
<source><![CDATA[Journal Mathematical Biology]]></source>
<year>1997</year>
<volume>35</volume>
<page-range>523-44</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Marcelo]]></surname>
<given-names><![CDATA[O]]></given-names>
</name>
<name>
<surname><![CDATA[Solari]]></surname>
<given-names><![CDATA[HG]]></given-names>
</name>
<name>
<surname><![CDATA[Schweigmann]]></surname>
<given-names><![CDATA[N]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A stochastic population dynamics model for Aedes aegypti: Formulation and application to a city with temperate climate]]></article-title>
<source><![CDATA[Bulletin of Mathematical Biology]]></source>
<year>2006</year>
</nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruiz]]></surname>
<given-names><![CDATA[RJ]]></given-names>
</name>
</person-group>
<source><![CDATA[Modelo estocástico de transmisión del dengue en poblaciones estructuradas]]></source>
<year>2004</year>
<publisher-loc><![CDATA[Colima, México ]]></publisher-loc>
<publisher-name><![CDATA[Tecoman]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Buratinni]]></surname>
<given-names><![CDATA[MN]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Chow]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<name>
<surname><![CDATA[Coutinho]]></surname>
<given-names><![CDATA[FAB]]></given-names>
</name>
<name>
<surname><![CDATA[Goh]]></surname>
<given-names><![CDATA[KT]]></given-names>
</name>
<name>
<surname><![CDATA[Lopez]]></surname>
<given-names><![CDATA[LF]]></given-names>
</name>
<name>
<surname><![CDATA[Ma]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<name>
<surname><![CDATA[Massad]]></surname>
<given-names><![CDATA[E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modelling the control strategies against dengue in Singapore]]></article-title>
<source><![CDATA[Epidemiology and Infection]]></source>
<year>2008</year>
<volume>136</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>309-19</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chowell]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
<name>
<surname><![CDATA[Diaz Dueñas]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Miller]]></surname>
<given-names><![CDATA[JC]]></given-names>
</name>
<name>
<surname><![CDATA[Alcazar Velazco]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<name>
<surname><![CDATA[Hyman]]></surname>
<given-names><![CDATA[JM]]></given-names>
</name>
<name>
<surname><![CDATA[Fenimore]]></surname>
<given-names><![CDATA[PW]]></given-names>
</name>
<name>
<surname><![CDATA[Castillo Chavez]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estimation of the reproduction number of dengue fever from spatial epidemic data]]></article-title>
<source><![CDATA[Mathematical Biosciences]]></source>
<year>2007</year>
<volume>208</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>571-89</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dumont]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
<name>
<surname><![CDATA[Chiroleu]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
<name>
<surname><![CDATA[Domerg]]></surname>
<given-names><![CDATA[C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On a temporal model for the Chikungunya disease: modeling, theory and numeric]]></article-title>
<source><![CDATA[Mathematical Biosciences]]></source>
<year>2008</year>
<volume>213</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>80-91</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bartley]]></surname>
<given-names><![CDATA[LM]]></given-names>
</name>
<name>
<surname><![CDATA[Donelly]]></surname>
<given-names><![CDATA[CA]]></given-names>
</name>
<name>
<surname><![CDATA[Garnett]]></surname>
<given-names><![CDATA[GP]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The seasonal pattern of dengue in endemic areas: Mathematical models of mechanisms]]></article-title>
<source><![CDATA[Journal Transactions of the Royal Society of Tropical Medicine and Hygiene]]></source>
<year>2002</year>
<volume>96</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>387-97</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[HM]]></given-names>
</name>
</person-group>
<source><![CDATA[Dinâmica da transmissão da dengue e delineamento de mecanismos de controle e prevenção]]></source>
<year>2010</year>
<page-range>63-89</page-range><publisher-name><![CDATA[UNICAMP/IMECC-DMA]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Newton]]></surname>
<given-names><![CDATA[EAC]]></given-names>
</name>
<name>
<surname><![CDATA[Reiter]]></surname>
<given-names><![CDATA[PA]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Model of the transmission of dengue fever with an evaluation of the impact of Ultra Low volume (ULV) insecticide applications on dengue epidemics]]></article-title>
<source><![CDATA[American Journal of Tropical Medicine and Hygiene]]></source>
<year>1992</year>
<volume>47</volume>
<page-range>709-20</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Greenhalgh]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some results on optimal control applied to epidemics, Mathematical]]></article-title>
<source><![CDATA[Biosciencie]]></source>
<year>1986</year>
<volume>88</volume>
<page-range>125-58</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gersovitz]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Hammer]]></surname>
<given-names><![CDATA[JS]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The economical control of infectious diseases]]></article-title>
<source><![CDATA[The Economic Journal]]></source>
<year>2004</year>
<volume>114</volume>
<page-range>1-27</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
