<?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>0121-7488</journal-id>
<journal-title><![CDATA[Ciencia en Desarrollo]]></journal-title>
<abbrev-journal-title><![CDATA[Ciencia en Desarrollo]]></abbrev-journal-title>
<issn>0121-7488</issn>
<publisher>
<publisher-name><![CDATA[Universidad Pedagógica y Tecnológica de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0121-74882025000100123</article-id>
<article-id pub-id-type="doi">10.19053/uptc.01217488.v16.n1.2025.17611</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Efecto de recaída y tratamientos recurrentes en salud mental para la dinámica poblacional del riesgo de suicidio]]></article-title>
<article-title xml:lang="en"><![CDATA[Effect of relapse and recurrent mental health treatments on the population dynamics of suicide risk]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Granada Díaz]]></surname>
<given-names><![CDATA[Héctor Andrés]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Nova Martínez]]></surname>
<given-names><![CDATA[Manuel Arturo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Olivar Robayo]]></surname>
<given-names><![CDATA[Luis Eduardo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Tolima Departamento de Matemáticas y Estadística ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Cooperativa de Colombia Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2025</year>
</pub-date>
<volume>16</volume>
<numero>1</numero>
<fpage>123</fpage>
<lpage>134</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0121-74882025000100123&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0121-74882025000100123&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0121-74882025000100123&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este artículo se propone una función para la tasa de riesgo de conductas suicidas, cuya formulación parte de la relación entre el riesgo, la ocurrencia de intentos de suicidio y el número de suicidios. Se muestra que la distribución de intentos de suicidio por edades en Colombia se ajusta a una función de distribución tipo Burr. Se caracterizan las poblaciones vulnerable, sin riesgo, susceptible en tratamiento y sin tratamiento, y se estiman series temporales con base en estadísticas colombianas del Dane, Minsalud y Sivigila. Para investigar las relaciones entre dichas poblaciones planteamos un modelo dinámico no lineal, con el cual se estima una proyección de la dinámica poblacional. El estado estacionario se analiza bajo técnicas numéricas llegando a identificar diferentes escenarios como focos estables, nodos estables y sillas, también se logra establecer las condiciones para alcanzar una bifurcación transcrítica que garantiza la coexistencia entre puntos de equilibrio y su evolución dinámica se examina sobre campos vectoriales tridimensionales. Los resultados sugieren que al implementar políticas de tratamiento efectivas podrían conllevar a la disminución de la tasa de riesgo, y controlando parámetros relacionados con el índice de recaída, podría la totalidad de población ser resistente a factores desencadenantes del suicidio.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This paper proposes a function for the risk rate of suicidal behavior, whose formulation is based on the relationship between risk, the occurrence of suicide attempts and the number of suicides. It is shown that the distribution of suicide attempts by age in Colombia adjusts to a Burr-type distribution function. Vulnerable, non risk, susceptible in treatment and untreated populations are characterized, and time series are estimated based on Colombian statistics from Dane, Minsalud and Sivigila. We propose a nonlinear dynamic model to investigate the relationships between these populations and use it to estimate a projection of population dynamics. The steady state is analyzed using numerical techniques, identifying scenarios such as stable focus, stable nodes and saddles. The conditions to reach a transcritical bifurcation that guarantees the coexistence between equilibrium points are established, and its dynamic evolution is examined on three-dimensional vector fields. The results suggest that implementing effective treatment policies could lead to a decrease in the risk rate, furthermore by controlling for parameters related to the relapse rate, the whole population could be resistant to suicide triggers factors.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Riesgo de suicidio]]></kwd>
<kwd lng="es"><![CDATA[Dinámica poblacional]]></kwd>
<kwd lng="es"><![CDATA[Modelo matemático]]></kwd>
<kwd lng="es"><![CDATA[Tratamiento]]></kwd>
<kwd lng="es"><![CDATA[Recaída]]></kwd>
<kwd lng="en"><![CDATA[Risk of suicide]]></kwd>
<kwd lng="en"><![CDATA[Population dynamics]]></kwd>
<kwd lng="en"><![CDATA[Mathematical model]]></kwd>
<kwd lng="en"><![CDATA[Treatment]]></kwd>
<kwd lng="en"><![CDATA[Relapse]]></kwd>
</kwd-group>
</article-meta>
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