<?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>2215-3470</journal-id>
<journal-title><![CDATA[Uniciencia]]></journal-title>
<abbrev-journal-title><![CDATA[Uniciencia]]></abbrev-journal-title>
<issn>2215-3470</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional, Costa Rica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2215-34702024000100274</article-id>
<article-id pub-id-type="doi">10.15359/ru.38-1.15</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Mathematical Modeling and Threshold Analysis of Acceptable Failure Rate and Academic Standard]]></article-title>
<article-title xml:lang="es"><![CDATA[Modelado matemático y análisis de umbral de tasa de reprobación aceptable y estándar académico]]></article-title>
<article-title xml:lang="pt"><![CDATA[Modelagem matemática e análise de limite de taxa de reprovação aceitável e padrão acadêmico]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ayotunde Ayoade]]></surname>
<given-names><![CDATA[Abayomi]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Manuel]]></surname>
<given-names><![CDATA[Mojisola]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ajoke Adeosun]]></surname>
<given-names><![CDATA[Motunrayo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,University of Lagos Faculty of Science Department of Mathematics]]></institution>
<addr-line><![CDATA[Lagos ]]></addr-line>
<country>Nigeria</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,University of Lagos Department of Arts and Social Sciences Education ]]></institution>
<addr-line><![CDATA[Lagos ]]></addr-line>
<country>Nigeria</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,University of Lagos Department of Adult Education ]]></institution>
<addr-line><![CDATA[Lagos ]]></addr-line>
<country>Nigeria</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<volume>38</volume>
<numero>1</numero>
<fpage>274</fpage>
<lpage>287</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702024000100274&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702024000100274&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702024000100274&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract A certificate is evidence of participating in a process, and anyone who holds a certificate is believed to have the prerequisites necessary to handle what the certificate qualifies them for. However, this perception might be incorrect if the certificate has been obtained by taking shortcuts.  (Objective)  In this paper, a compartmental model was developed to quantify factors that could put the authenticity of a certificate in doubt by examining the trade-off between academic standards and failure rates in the context of tertiary education institutions in Nigeria.  (Methodology)  The model was validated using several mathematical theorems. Equilibria for the model and the threshold for acceptable academic performance were derived. Stability analysis was carried out by using the stability theory of differential equations based on the derived acceptable academic performance threshold.  (Results)  The theoretical results for the model were validated through numerical simulations, and the results from the simulations linked acceptable failure rates to academic performance falling below the threshold of the institutions&#8217; standards.  (Conclusions)  The policy implication of the result is that an increase in the supply of qualified graduates into Nigeria&#8217;s labor markets, as well as a reduction in the rate of unemployment, is a function of maintaining academic standards.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El certificado es una evidencia de participación en un proceso y se cree que cualquier persona que posea uno tiene un requisito previo para manejar todo aquello para lo que este califica. Sin embargo, la impresión podría fallar, si el certificado se hubiera obtenido tomando atajos.  (Objetivo)  En este documento se desarrolló un modelo compartimental para cuantificar los factores que podrían poner en duda la autenticidad de un certificado, mediante el examen de la compensación entre el estándar académico y las tasas de reprobación, en el contexto de las instituciones de educación terciaria en Nigeria.  (Metodología)  El modelo se demostró válido utilizando algunos amplios teoremas matemáticos. Se derivaron los equilibrios para dicho método y el umbral para un rendimiento académico aceptable. El análisis de estabilidad se llevó a cabo empleando la teoría de la estabilidad de ecuaciones diferenciales, basada en el umbral de rendimiento académico ace ptable obtenido.  (Resultados)  Los resultados teóricos del modelo fueron validados por medio de simulaciones numéricas y los de las simulaciones vincularon la tasa de reprobación aceptable con el rendimiento académico que cayó por debajo del umbral del estándar establecido por las instituciones.  (Conclusiones)  La implicación política del resultado es que el aumento en la oferta de graduados calificados en los mercados laborales de Nigeria, así como la reducción en la tasa de desempleo, son una función del mantenimie nto de los estándares académicos.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O certificado é uma prova de participação em um processo e acredita-se que quem o possui tem como pré-requisito realizar tudo para o qual o referido certific ado o qualifica. No entanto, a impressão poderia falhar se o certificado tivesse sido obtido através de atalhos.  (Objetivo)  Neste artigo, foi desenvolvido um modelo compartimental para quantificar fatores que poderiam pôr em dúvida a autenticidade de um certificado, examinando o compromisso entre o padrão académico e as taxas de reprovação no contexto de instituições terciárias referenciadas na Nigéria.  (Metodologia) O modelo foi provado válido usando alguns teoremas matemáticos amplos. Os equilíbrios para o modelo e o limite para desempenho acadêmico aceitável foram derivados. A análise de estabilidade foi realizada utilizando a teoria da estabilidade de equações diferenciais com base no limite de desempenho acadêmico aceitável derivado.  (Resultados)  Os resultados teóricos do modelo foram validados por meio de simulações numéricas e os resultados das simulações relacionaram a taxa de reprovação aceitável com o desempenho acadêmico que ficou abaixo do limite do padrão estabelecido pelas instituições.  (Conclusões)  A implicação política do resultado é que o aumento da oferta de licenciados qualificados nos mercados de trabalho nigerianos, bem como a redução da taxa de desemprego, é uma função da manutenção dos padrões académicos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[certificate]]></kwd>
<kwd lng="en"><![CDATA[compartmental model]]></kwd>
<kwd lng="en"><![CDATA[academic standard]]></kwd>
<kwd lng="en"><![CDATA[failure rates]]></kwd>
<kwd lng="en"><![CDATA[tertiary education]]></kwd>
<kwd lng="es"><![CDATA[certificado]]></kwd>
<kwd lng="es"><![CDATA[modelo compartimentado]]></kwd>
<kwd lng="es"><![CDATA[estándar académico]]></kwd>
<kwd lng="es"><![CDATA[tasas de reprobación]]></kwd>
<kwd lng="es"><![CDATA[instituciones de educación terciaria]]></kwd>
<kwd lng="pt"><![CDATA[certificado]]></kwd>
<kwd lng="pt"><![CDATA[modelo compartimental]]></kwd>
<kwd lng="pt"><![CDATA[padrão acadêmico]]></kwd>
<kwd lng="pt"><![CDATA[taxas de reprovação]]></kwd>
<kwd lng="pt"><![CDATA[instituições terciárias]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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