<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332019000100139</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v26i1.35529</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[The role of short-term immigration on disease dynamics: an sir model with age-structure]]></article-title>
<article-title xml:lang="es"><![CDATA[El rol de la immigración en periodos cortos sobre la dinámica de enfermedades: un modelo sir con estructura de edad]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sánchez]]></surname>
<given-names><![CDATA[Fabio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Calvo]]></surname>
<given-names><![CDATA[Juan G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<volume>26</volume>
<numero>1</numero>
<fpage>139</fpage>
<lpage>159</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332019000100139&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332019000100139&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332019000100139&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract [14] We formulate an age-structured nonlinear partial differential equation model that features short-term immigration effects in a population. In- dividuals can immigrate into the population as any of the three stages in the model: susceptible, infected or recovered. Global stability of the immigration-free and infection-free equilibria is discussed. A generalized numerical framework is established and specific short-term immigration scenarios are explored.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen [18] Se formula un modelo de ecuaciones diferenciales parciales no lineal y con estructura de edad, que incluye inmigración en un periodo breve de tiempo y sus efectos en la población. Los inmigrantes pueden ser de cualquier clase en el modelo: susceptibles, infectados o recuperados. Se discute además la estabilidad global del equilibrio correspondiente al mo- delo libre de infección e inmigración. Un método numérico general es discutido, y se exploran escenarios específicos con inmigración en perio- dos cortos de tiempo.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[age-structured model]]></kwd>
<kwd lng="en"><![CDATA[epidemic models]]></kwd>
<kwd lng="en"><![CDATA[immigration]]></kwd>
<kwd lng="en"><![CDATA[migratory effects]]></kwd>
<kwd lng="en"><![CDATA[finite difference methods]]></kwd>
<kwd lng="es"><![CDATA[modelo con estructura de edad]]></kwd>
<kwd lng="es"><![CDATA[modelos epidémicos]]></kwd>
<kwd lng="es"><![CDATA[inmi- gración]]></kwd>
<kwd lng="es"><![CDATA[efectos migratorios]]></kwd>
<kwd lng="es"><![CDATA[métodos de diferencias finitas]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Allen]]></surname>
<given-names><![CDATA[L. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Brauer]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Van den Driessche]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Wu]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Epidemiology]]></source>
<year>2008</year>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Alvarado]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Costa Rica once again un- der malaria alert]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<collab>American Community Survey</collab>
<source><![CDATA[]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="">
<collab>BBC News.</collab>
<source><![CDATA[Migrant caravan: what is it and why does it matter?]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="">
<collab>BBC News</collab>
<source><![CDATA[Puerto Rico increases hurricane Maria death toll to 2,975]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="">
<collab>BBC News.</collab>
<source><![CDATA[Venezuela&#8217;s migration crisis: is enough being done?]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="">
<collab>Center for Disease Control and Prevention</collab>
<source><![CDATA[]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="">
<collab>Center for Disease Control and Prevention</collab>
<source><![CDATA[Entomology &amp; ecology]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="">
<collab>Center for Disease Control and Prevention</collab>
<source><![CDATA[&#8220;Immi- grant and refugee health]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Franceschetti]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Pugliese]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Threshold behaviour of a SIR epi- demic model with age structure and immigration]]></article-title>
<source><![CDATA[Journal of Mathemati- cal Biology]]></source>
<year>2008</year>
<volume>57</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-27</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hanson]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[4 charts show Venezuela&#8217;s worsen- ing migrant crisis]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hirschman]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The contributions of immigrants to american cul- ture]]></article-title>
<source><![CDATA[Daedalus]]></source>
<year>2013</year>
<volume>142</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>26-47</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Holmes]]></surname>
<given-names><![CDATA[E.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Lewis]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Banks]]></surname>
<given-names><![CDATA[J.E.]]></given-names>
</name>
<name>
<surname><![CDATA[Veit]]></surname>
<given-names><![CDATA[R.R. (]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Partial differ- ential equations in ecology: spatial interactions and population dynamics]]></article-title>
<source><![CDATA[Ecology]]></source>
<year>1994</year>
<volume>75</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>17-29</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kribs-Zaleta]]></surname>
<given-names><![CDATA[C.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Martcheva]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Vaccination strategies and backward bifurcation in an age-since-infection structured model]]></article-title>
<source><![CDATA[Mathe- matical Biosciences]]></source>
<year>2002</year>
<volume>177-178</volume>
<page-range>317-32</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martcheva]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Thieme]]></surname>
<given-names><![CDATA[H.R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Progression age enhanced back- ward bifurcation in an epidemic model with super-infection]]></article-title>
<source><![CDATA[Journal of Mathematical Biology]]></source>
<year>2003</year>
<volume>46</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>385-424</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[McKitterick]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Number of criminals in migrant cara- van - does it matter?]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Meléndez]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Hinojosa]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Estimates of post-hurricane Maria exodus from Puerto Rico]]></source>
<year>2017</year>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="">
<collab>Migration Policy Institute</collab>
<source><![CDATA[Profile of the unauthorized population: United States]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[O&#8217;Brien]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[The migrant caravan and public health]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sanchez]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Calvo]]></surname>
<given-names><![CDATA[J.G.]]></given-names>
</name>
<name>
<surname><![CDATA[Segura]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Feng]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<source><![CDATA[A partial differ- ential equation model with age-structure and nonlinear recidivism: condi- tions for a backward bifurcation and a general numerical implementation]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sands]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[This year saw the most people in immigration deten- tion since 2001]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Semple]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Nicaraguan migrants fleeing turmoil test Costa Rica&#8217;s good will]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shim]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Feng]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Martcheva]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Castillo-Chavez]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An age- structured epidemic model of rotavirus with vaccination]]></article-title>
<source><![CDATA[Journal of Math- ematical Biology]]></source>
<year>2006</year>
<volume>53</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>719-46</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schofield]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[What next after the jungle?]]></source>
<year>2016</year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
