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    "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">Introducci&#243;n</span><p id="par0005" class="elsevierStylePara elsevierViewall">Durante la crisis de salud internacional provocada por la pandemia de COVID-19 se hace necesario no solo conocer los datos sobre contagios&#44; muertes y ocupaci&#243;n hospitalaria&#44; sino tambi&#233;n hacer predicciones que ayuden a la propia gesti&#243;n de la crisis por parte de las autoridades sanitarias&#46;</p><p id="par0010" class="elsevierStylePara elsevierViewall">El presente trabajo tiene como objetivo describir la metodolog&#237;a utilizada para la elaboraci&#243;n de modelos predictivos de contagios y defunciones para la epidemia de COVID-19 en Espa&#241;a&#46; Los datos utilizados&#44; desde el 4 de marzo hasta el 22 de abril de 2020&#44; fueron los datos oficiales que ofrec&#237;a diariamente el Ministerio de Sanidad de Espa&#241;a<a class="elsevierStyleCrossRef" href="#bib0055"><span class="elsevierStyleSup">1</span></a>&#46;&#63;</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0030">Exposici&#243;n del m&#233;todo</span><p id="par0015" class="elsevierStylePara elsevierViewall">Para las modelizaciones se sigui&#243; el siguiente esquema&#44; simplificaci&#243;n del descrito por Lega y Brown<a class="elsevierStyleCrossRef" href="#bib0060"><span class="elsevierStyleSup">2</span></a>&#58;<ul class="elsevierStyleList" id="lis0005"><li class="elsevierStyleListItem" id="lsti0005"><span class="elsevierStyleLabel">&#8226;</span><p id="par0020" class="elsevierStylePara elsevierViewall">Paso 1&#58; se ajustaron los valores acumulados a una curva <span class="elsevierStyleItalic">G&#40;t&#41;</span> &#40;<a class="elsevierStyleCrossRef" href="#fig0005">fig&#46; 1</a>&#44; curva de casos acumulados&#41;&#46;</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia></li><li class="elsevierStyleListItem" id="lsti0010"><span class="elsevierStyleLabel">&#8226;</span><p id="par0025" class="elsevierStylePara elsevierViewall">Paso 2&#58; se calcul&#243; la primera derivada <span class="elsevierStyleItalic">g&#40;t&#41;</span> de la curva anterior &#40;<a class="elsevierStyleCrossRef" href="#fig0005">fig&#46; 1</a>&#44; curva de casos diarios&#41;&#46;</p></li></ul></p><p id="par0030" class="elsevierStylePara elsevierViewall">Con los datos acumulados diarios se calcul&#243; la curva de Gompertz<a class="elsevierStyleCrossRef" href="#bib0065"><span class="elsevierStyleSup">3</span></a>&#63; de tres par&#225;metros que mejor se ajustaba en cada caso a los datos&#58;<elsevierMultimedia ident="eq0005"></elsevierMultimedia></p><p id="par0035" class="elsevierStylePara elsevierViewall">Se utiliz&#243; el modelo de crecimiento de Gompertz en lugar de otros&#44; como el log&#237;stico o el de Bertalanffy&#44; por haber demostrado ser algo m&#225;s preciso para predecir los casos acumulados fuera de la provincia china de Hubei<a class="elsevierStyleCrossRef" href="#bib0070"><span class="elsevierStyleSup">4</span></a>&#63;&#44; lugar donde se origin&#243; la pandemia de COVID-19&#46;</p><p id="par0040" class="elsevierStylePara elsevierViewall">Para el ajuste de la curva de Gompertz a los datos acumulados observados se usaron los algoritmos de Nelter-Mead<a class="elsevierStyleCrossRef" href="#bib0075"><span class="elsevierStyleSup">5</span></a>&#63; 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lo que puede interpretarse como el &#171;horizonte&#187; de la epidemia&#44; esto es&#44; el n&#250;mero de casos esperados al final de esta&#46;</p><p id="par0055" class="elsevierStylePara elsevierViewall">La primera derivada de la funci&#243;n anterior<a class="elsevierStyleCrossRef" href="#bib0095"><span class="elsevierStyleSup">9</span></a>&#44; la interpretamos como la curva del n&#250;mero de casos diarios&#58;<elsevierMultimedia ident="eq0010"></elsevierMultimedia></p><p id="par0060" class="elsevierStylePara elsevierViewall">A trav&#233;s de ella se pueden calcular los valores esperados los d&#237;as futuros&#46; El punto donde esta funci&#243;n alcanza el m&#225;ximo puede interpretarse como el pico de la epidemia&#46;</p></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0035">Aplicaci&#243;n pr&#225;ctica</span><p id="par0065" class="elsevierStylePara elsevierViewall">En el momento en que se publican nuevos datos diarios se vuelve a calcular un modelo seg&#250;n el esquema anterior para los contagios y otro para las defunciones en cada comunidad aut&#243;noma y para el total del pa&#237;s&#46;</p><p id="par0070" class="elsevierStylePara elsevierViewall">Para el presente trabajo se calcularon 50 modelos de contagios y 50 de fallecimientos para cada una de las comunidades aut&#243;nomas &#40;dos modelos diarios&#44; desde el 4 de marzo hasta el 22 de abril&#44; cada d&#237;a un modelo&#41;&#46;</p><p id="par0075" class="elsevierStylePara elsevierViewall">Seg&#250;n esta metodolog&#237;a&#44; el pico de contagios se alcanz&#243; en Espa&#241;a aproximadamente a finales de marzo&#44; mientras que el pico de defunciones se estim&#243; a primeros de abril de 2020&#46; Los resultados concretos de los picos de las curvas&#44; adem&#225;s de los horizontes&#44; pueden consultarse en la app interactiva&#58; <a href="https://www.easp.edu.es/data-apps/covid-easp/covid19_ESP/">https&#58;&#47;&#47;www&#46;easp&#46;edu&#46;es&#47;data-apps&#47;covid-easp&#47;covid19&#95;ESP&#47;</a></p><p id="par0080" class="elsevierStylePara elsevierViewall">La <a class="elsevierStyleCrossRef" href="#fig0010">figura 2</a> muestra la evoluci&#243;n de los horizontes &#40;coeficientes <span class="elsevierStyleItalic">a</span> de los modelos&#41; que se fueron calculando diariamente y a lo largo del tiempo&#46; A modo de ejemplo&#44; los modelos predec&#237;an m&#225;s de 900&#46;000 casos de contagio y unas 67&#46;000 muertes en torno al 27 de marzo para el total de Espa&#241;a&#44; y a medida que se sucedieron los d&#237;as estos horizontes estimados descendieron hasta situarse alrededor de 240&#46;000 contagios y 25&#46;000 fallecidos&#46; A partir de los primeros d&#237;as de abril&#44; esas estimaciones permanecen estables a lo largo del tiempo&#46; De manera general se observa que&#44; en todos los casos&#44; al principio el comportamiento de la serie de horizontes era algo err&#225;tica&#44; pero a medida que avanzaron los d&#237;as el par&#225;metro fue estabiliz&#225;ndose&#44; lo cual se puede interpretar como medida de robustez de la estimaci&#243;n del n&#250;mero de contagiados y de fallecidos para cada comunidad aut&#243;noma&#46;</p><elsevierMultimedia ident="fig0010"></elsevierMultimedia><p id="par0085" class="elsevierStylePara elsevierViewall">A partir de las curvas de contagios diarios y de defunciones diarias <span class="elsevierStyleItalic">&#40;g&#40;t&#41;&#41;</span> se hizo una estimaci&#243;n de las fechas en que no se observar&#225;n m&#225;s contagios ni m&#225;s defunciones &#40;<a class="elsevierStyleCrossRef" href="#tbl0005">tabla 1</a>&#41;&#46; Hay que hacer notar que tanto las predicciones de estas fechas como las de los horizontes son orientativas y no ser&#225;n precisas si la situaci&#243;n epidemiol&#243;gica var&#237;a sustancialmente&#46;</p><elsevierMultimedia ident="tbl0005"></elsevierMultimedia></span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0040">Conclusiones</span><p id="par0090" class="elsevierStylePara elsevierViewall">Presentamos en este trabajo una metodolog&#237;a de f&#225;cil uso para modelizar epidemias como la de COVID-19&#46; Consideramos que en esta sencillez radica su fortaleza&#44; ya que se utilizan exclusivamente los datos sobre contagios y defunciones que despu&#233;s se predicen&#44; sin contar con ning&#250;n tipo de covariable externa para su c&#225;lculo&#46; Esto&#44; por una parte&#44; podr&#237;a parecer una debilidad al no a&#241;adir m&#225;s informaci&#243;n a los modelos&#44; pero as&#237; se evita el ruido que podr&#237;an introducir esas hipot&#233;ticas variables externas&#46; Por otra parte&#44; la ausencia de m&#225;s informaci&#243;n hace que la calidad de las predicciones dependa mucho de la calidad de los datos&#46;</p><p id="par0095" class="elsevierStylePara elsevierViewall">Hay que tener en cuenta que las predicciones de los modelos de contagios&#44; sobre todo a partir de aproximadamente la tercera semana de abril de 2020&#44; pueden sufrir grandes variaciones con respecto a los valores observados por los cambios en la definici&#243;n de caso&#46; No ocurre lo mismo con respecto a los modelos de defunciones&#44; que son m&#225;s robustos a lo largo del tiempo al no haber sufrido grandes cambios en su definici&#243;n&#46;</p><p id="par0100" class="elsevierStylePara elsevierViewall">Con respecto a las fechas estimadas del fin de la epidemia en cada comunidad aut&#243;noma&#44; hay que tener en cuenta que son estimaciones aproximadas y que pueden sufrir alteraciones si se producen cambios bruscos en las tendencias&#46; De hecho&#44; los modelos predec&#237;an horizontes de muchos m&#225;s casos y defunciones a finales de marzo que a partir de la segunda quincena de abril&#44; lo que puede deberse a las medidas de confinamiento tomadas por las autoridades&#44; que tienen un efecto en las curvas de la epidemia a partir de al menos una semana desde su implantaci&#243;n<a class="elsevierStyleCrossRef" href="#bib0100"><span class="elsevierStyleSup">10</span></a>&#63;&#46;</p><p id="par0105" class="elsevierStylePara elsevierViewall">En cuanto al fin de la epidemia&#44; las fechas en las que se espera que no haya defunciones son anteriores a las fechas en las que se espera que no haya contagios&#44; y esto tiene mucho sentido dado que no todas las personas contagiadas fallecer&#225;n y que el porcentaje de personas que sobreviven a la enfermedad es mucho mayor que el de las personas que fallecen&#46;</p><p id="par0110" class="elsevierStylePara elsevierViewall">En cualquier caso&#44; en este trabajo presentamos una metodolog&#237;a utilizada para modelizar la epidemia de COVID-19 en Espa&#241;a y en sus comunidades aut&#243;nomas&#44; y el valor que le damos es referente al contexto temporal de la epidemia&#44; aunque somos conscientes de que pasada la crisis esta metodolog&#237;a puede ser matizada&#46;</p></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0045">Editor responsable del art&#237;culo</span><p id="par0115" class="elsevierStylePara elsevierViewall">Carlos &#193;lvarez Dardet&#46;</p></span><span id="sec0030" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0050">Contribuciones de autor&#237;a</span><p id="par0120" class="elsevierStylePara elsevierViewall">Los dos autores han contribuido a la concepci&#243;n del estudio&#44; la redacci&#243;n del manuscrito y la revisi&#243;n de las distintas versiones&#46; P&#46; S&#225;nchez Villegas realiz&#243; los an&#225;lisis de los datos&#46; Ambos se hacen responsables del contenido &#237;ntegro del trabajo&#46;</p></span><span id="sec0035" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0055">Financiaci&#243;n</span><p id="par0125" class="elsevierStylePara elsevierViewall">Ninguna&#46;</p></span><span id="sec0040" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0060">Conflicto de intereses</span><p id="par0130" class="elsevierStylePara elsevierViewall">Ninguno&#46;</p></span></span>"
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        "resumen" => "<span id="abst0005" class="elsevierStyleSection elsevierViewall"><p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">Durante la crisis de salud internacional provocada por la pandemia de COVID-19&#44; adem&#225;s de conocer los datos sobre contagios&#44; muertes y ocupaci&#243;n de camas hospitalarias tambi&#233;n es necesario hacer predicciones que ayuden a la gesti&#243;n de la crisis por parte de las autoridades sanitarias&#46; El presente trabajo tiene como objetivo describir la metodolog&#237;a utilizada para la elaboraci&#243;n de modelos predictivos de contagios y defunciones para la epidemia de COVID-19 en Espa&#241;a basados en curvas de Gompertz&#46; La metodolog&#237;a se aplica al total del pa&#237;s y a cada una de sus comunidades aut&#243;nomas&#46; De acuerdo con los datos oficiales publicados a la fecha de realizaci&#243;n de este trabajo&#44; y a trav&#233;s de los modelos descritos&#44; estimamos un total de alrededor de 240&#46;000 contagiados y 25&#46;000 fallecidos al final de la epidemia&#46; Pronosticamos el final de la epidemia entre los meses de junio y julio de 2020&#46;</p></span>"
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        "resumen" => "<span id="abst0010" class="elsevierStyleSection elsevierViewall"><p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">During the international health crisis caused by the COVID-19 pandemic&#44; it is necessary not only to know the data on infections&#44; deaths and the occupation of hospital beds&#44; but also to make predictions that help health authorities in the management of the crisis&#46; The present work aims to describe the methodology used to develop predictive models of infections and deaths for the COVID-19 epidemic in Spain&#44; based on Gompertz curves&#46; The methodology is applied to the country as a whole and to each of its Autonomous Communities&#46; Based on the official data available on the date of this work&#44; and through the models described&#44; we estimate a total of around 240&#46;000 infected and 25&#46;000 deaths at the end of the epidemic&#46; At a national level&#44; we forecast the end of the epidemic between June and July 2020&#46;</p></span>"
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                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2727&#46;282 &#40;2628&#46;178&#44;2826&#46;386&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">25&#46;458 &#40;24&#46;83&#44;26&#46;086&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t\ttop\n
                  \t\t\t\t">09&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;061 &#40;-0&#46;066&#44;-0&#46;056&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">351&#46;555 &#40;319&#46;567&#44;383&#46;542&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">38&#46;859 &#40;37&#46;219&#44;40&#46;5&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">05&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Baleares&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;116 &#40;-0&#46;124&#44;-0&#46;107&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">1828&#46;794 &#40;1779&#46;225&#44;1878&#46;363&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">23&#46;256 &#40;22&#46;857&#44;23&#46;654&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">15&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;075 &#40;-0&#46;083&#44;-0&#46;067&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">223&#46;425 &#40;203&#46;344&#44;243&#46;506&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">34&#46;923 &#40;33&#46;49&#44;36&#46;356&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">18&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Canarias&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;121 &#40;-0&#46;126&#44;-0&#46;116&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2169&#46;584 &#40;2139&#46;665&#44;2199&#46;502&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">22&#46;922 &#40;22&#46;719&#44;23&#46;126&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">14&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;123 &#40;-0&#46;135&#44;-0&#46;112&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">123&#46;78 &#40;119&#46;256&#44;128&#46;304&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">26&#46;745 &#40;26&#46;271&#44;27&#46;22&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">23&#47;04&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Cantabria&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;113 &#40;-0&#46;125&#44;-0&#46;102&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2140&#46;596 &#40;2056&#46;683&#44;2224&#46;509&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">24&#46;561 &#40;24&#46;002&#44;25&#46;12&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">18&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;081 &#40;-0&#46;089&#44;-0&#46;074&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">219&#46;775 &#40;203&#46;95&#44;235&#46;599&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">34&#46;6 &#40;33&#46;519&#44;35&#46;681&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">16&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Castilla-La Mancha&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;088 &#40;-0&#46;092&#44;-0&#46;085&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">20389&#46;014 &#40;19938&#46;915&#44;20839&#46;113&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">29&#46;434 &#40;29&#46;107&#44;29&#46;762&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">29&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;083 &#40;-0&#46;086&#44;-0&#46;079&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2619&#46;466 &#40;2538&#46;272&#44;2700&#46;66&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">31&#46;887 &#40;31&#46;413&#44;32&#46;362&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">12&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Castilla y Le&#243;n&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;069 &#40;-0&#46;073&#44;-0&#46;064&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">22078&#46;697 &#40;20977&#46;38&#44;23180&#46;014&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">31&#46;945 &#40;31&#46;061&#44;32&#46;829&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">24&#47;07&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;107 &#40;-0&#46;109&#44;-0&#46;105&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">1715&#46;048 &#40;1698&#46;215&#44;1731&#46;88&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">29&#46;785 &#40;29&#46;657&#44;29&#46;914&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">24&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Catalu&#241;a&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;086 &#40;-0&#46;09&#44;-0&#46;081&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">49227&#46;704 &#40;47679&#46;816&#44;50775&#46;591&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">27&#46;969 &#40;27&#46;476&#44;28&#46;462&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">10&#47;07&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;129 &#40;-0&#46;134&#44;-0&#46;123&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">4313&#46;684 &#40;4238&#46;415&#44;4388&#46;953&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">27&#46;729 &#40;27&#46;507&#44;27&#46;95&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">22&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Ceuta&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;157 &#40;-0&#46;183&#44;-0&#46;131&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">115&#46;651 &#40;109&#46;642&#44;121&#46;66&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">28&#46;416 &#40;27&#46;846&#44;28&#46;987&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">-0&#46;262 &#40;-0&#46;393&#44;-0&#46;131&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">30&#46;558 &#40;29&#46;353&#44;31&#46;763&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">C&#46; Valenciana&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;099 &#40;-0&#46;105&#44;-0&#46;094&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">11321&#46;285 &#40;11039&#46;421&#44;11603&#46;15&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">25&#46;324 &#40;24&#46;954&#44;25&#46;694&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;095 &#40;-0&#46;099&#44;-0&#46;091&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">1295&#46;589 &#40;1265&#46;824&#44;1325&#46;353&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">30&#46;546 &#40;30&#46;225&#44;30&#46;867&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">27&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Extremadura&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;085 &#40;-0&#46;095&#44;-0&#46;074&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">3688&#46;372 &#40;3434&#46;953&#44;3941&#46;79&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;766 &#40;25&#46;66&#44;27&#46;873&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;107 &#40;-0&#46;113&#44;-0&#46;102&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">446&#46;697 &#40;434&#46;893&#44;458&#46;501&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">29&#46;8 &#40;29&#46;454&#44;30&#46;146&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">11&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Galicia&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;118 &#40;-0&#46;123&#44;-0&#46;113&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">8960&#46;746 &#40;8820&#46;319&#44;9101&#46;173&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;091 &#40;25&#46;881&#44;26&#46;302&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;102 &#40;-0&#46;106&#44;-0&#46;097&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">429&#46;271 &#40;418&#46;027&#44;440&#46;516&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">32&#46;36 &#40;32&#46;024&#44;32&#46;697&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">15&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Madrid&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;079 &#40;-0&#46;085&#44;-0&#46;074&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">67301&#46;118 &#40;64827&#46;97&#44;69774&#46;266&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;79 &#40;26&#46;183&#44;27&#46;397&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;098 &#40;-0&#46;101&#44;-0&#46;096&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">8196&#46;958 &#40;8097&#46;911&#44;8296&#46;005&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;119 &#40;25&#46;941&#44;26&#46;297&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">09&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Melilla&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;086 &#40;-0&#46;095&#44;-0&#46;077&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">125&#46;585 &#40;119&#46;102&#44;132&#46;067&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">24&#46;356 &#40;23&#46;502&#44;25&#46;211&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;23 &#40;-0&#46;282&#44;-0&#46;177&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">2&#46;059 &#40;1&#46;949&#44;2&#46;17&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">24&#46;6 &#40;23&#46;781&#44;25&#46;42&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">13&#47;04&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Murcia&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;111 &#40;-0&#46;119&#44;-0&#46;103&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">1753&#46;878 &#40;1707&#46;227&#44;1800&#46;529&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">23&#46;685 &#40;23&#46;296&#44;24&#46;073&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">16&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;132 &#40;-0&#46;14&#44;-0&#46;125&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">131&#46;682 &#40;128&#46;555&#44;134&#46;809&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">30&#46;778 &#40;30&#46;505&#44;31&#46;051&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">27&#47;04&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Navarra&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">-0&#46;083 &#40;-0&#46;087&#44;-0&#46;08&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">5570&#46;162 &#40;5450&#46;229&#44;5690&#46;095&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">26&#46;716 &#40;26&#46;369&#44;27&#46;063&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">15&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
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Nota metodológica
Modelos predictivos de la epidemia de COVID-19 en España con curvas de Gompertz
Predictive models of the COVID-19 epidemic in Spain with Gompertz curves
Pablo Sánchez-Villegasa,b,c,
Corresponding author
pablosvillegas@gmail.com

Autor para correspondencia.
, Antonio Daponte Codinaa,b,c
a Escuela Andaluza de Salud Pública, Granada, España
b Observatorio de Salud y Medio Ambiente de Andalucía (OSMAN), Granada, España
c CIBER de Epidemiología y Salud Pública (CIBERESP), España
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    "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">Introducci&#243;n</span><p id="par0005" class="elsevierStylePara elsevierViewall">Durante la crisis de salud internacional provocada por la pandemia de COVID-19 se hace necesario no solo conocer los datos sobre contagios&#44; muertes y ocupaci&#243;n hospitalaria&#44; sino tambi&#233;n hacer predicciones que ayuden a la propia gesti&#243;n de la crisis por parte de las autoridades sanitarias&#46;</p><p id="par0010" class="elsevierStylePara elsevierViewall">El presente trabajo tiene como objetivo describir la metodolog&#237;a utilizada para la elaboraci&#243;n de modelos predictivos de contagios y defunciones para la epidemia de COVID-19 en Espa&#241;a&#46; Los datos utilizados&#44; desde el 4 de marzo hasta el 22 de abril de 2020&#44; fueron los datos oficiales que ofrec&#237;a diariamente el Ministerio de Sanidad de Espa&#241;a<a class="elsevierStyleCrossRef" href="#bib0055"><span class="elsevierStyleSup">1</span></a>&#46;&#63;</p></span><span id="sec0010" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0030">Exposici&#243;n del m&#233;todo</span><p id="par0015" class="elsevierStylePara elsevierViewall">Para las modelizaciones se sigui&#243; el siguiente esquema&#44; simplificaci&#243;n del descrito por Lega y Brown<a class="elsevierStyleCrossRef" href="#bib0060"><span class="elsevierStyleSup">2</span></a>&#58;<ul class="elsevierStyleList" id="lis0005"><li class="elsevierStyleListItem" id="lsti0005"><span class="elsevierStyleLabel">&#8226;</span><p id="par0020" class="elsevierStylePara elsevierViewall">Paso 1&#58; se ajustaron los valores acumulados a una curva <span class="elsevierStyleItalic">G&#40;t&#41;</span> &#40;<a class="elsevierStyleCrossRef" href="#fig0005">fig&#46; 1</a>&#44; curva de casos acumulados&#41;&#46;</p><elsevierMultimedia ident="fig0005"></elsevierMultimedia></li><li class="elsevierStyleListItem" id="lsti0010"><span class="elsevierStyleLabel">&#8226;</span><p id="par0025" class="elsevierStylePara elsevierViewall">Paso 2&#58; se calcul&#243; la primera derivada <span class="elsevierStyleItalic">g&#40;t&#41;</span> de la curva anterior &#40;<a class="elsevierStyleCrossRef" href="#fig0005">fig&#46; 1</a>&#44; curva de casos diarios&#41;&#46;</p></li></ul></p><p id="par0030" class="elsevierStylePara elsevierViewall">Con los datos acumulados diarios se calcul&#243; la curva de Gompertz<a class="elsevierStyleCrossRef" href="#bib0065"><span class="elsevierStyleSup">3</span></a>&#63; de tres par&#225;metros que mejor se ajustaba en cada caso a los datos&#58;<elsevierMultimedia ident="eq0005"></elsevierMultimedia></p><p id="par0035" class="elsevierStylePara elsevierViewall">Se utiliz&#243; el modelo de crecimiento de Gompertz en lugar de otros&#44; como el log&#237;stico o el de Bertalanffy&#44; por haber demostrado ser algo m&#225;s preciso para predecir los casos acumulados fuera de la provincia china de Hubei<a class="elsevierStyleCrossRef" href="#bib0070"><span class="elsevierStyleSup">4</span></a>&#63;&#44; lugar donde se origin&#243; la pandemia de COVID-19&#46;</p><p id="par0040" class="elsevierStylePara elsevierViewall">Para el ajuste de la curva de Gompertz a los datos acumulados observados se usaron los algoritmos de Nelter-Mead<a class="elsevierStyleCrossRef" href="#bib0075"><span class="elsevierStyleSup">5</span></a>&#63; 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lo que puede interpretarse como el &#171;horizonte&#187; de la epidemia&#44; esto es&#44; el n&#250;mero de casos esperados al final de esta&#46;</p><p id="par0055" class="elsevierStylePara elsevierViewall">La primera derivada de la funci&#243;n anterior<a class="elsevierStyleCrossRef" href="#bib0095"><span class="elsevierStyleSup">9</span></a>&#44; la interpretamos como la curva del n&#250;mero de casos diarios&#58;<elsevierMultimedia ident="eq0010"></elsevierMultimedia></p><p id="par0060" class="elsevierStylePara elsevierViewall">A trav&#233;s de ella se pueden calcular los valores esperados los d&#237;as futuros&#46; El punto donde esta funci&#243;n alcanza el m&#225;ximo puede interpretarse como el pico de la epidemia&#46;</p></span><span id="sec0015" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0035">Aplicaci&#243;n pr&#225;ctica</span><p id="par0065" class="elsevierStylePara elsevierViewall">En el momento en que se publican nuevos datos diarios se vuelve a calcular un modelo seg&#250;n el esquema anterior para los contagios y otro para las defunciones en cada comunidad aut&#243;noma y para el total del pa&#237;s&#46;</p><p id="par0070" class="elsevierStylePara elsevierViewall">Para el presente trabajo se calcularon 50 modelos de contagios y 50 de fallecimientos para cada una de las comunidades aut&#243;nomas &#40;dos modelos diarios&#44; desde el 4 de marzo hasta el 22 de abril&#44; cada d&#237;a un modelo&#41;&#46;</p><p id="par0075" class="elsevierStylePara elsevierViewall">Seg&#250;n esta metodolog&#237;a&#44; el pico de contagios se alcanz&#243; en Espa&#241;a aproximadamente a finales de marzo&#44; mientras que el pico de defunciones se estim&#243; a primeros de abril de 2020&#46; Los resultados concretos de los picos de las curvas&#44; adem&#225;s de los horizontes&#44; pueden consultarse en la app interactiva&#58; <a href="https://www.easp.edu.es/data-apps/covid-easp/covid19_ESP/">https&#58;&#47;&#47;www&#46;easp&#46;edu&#46;es&#47;data-apps&#47;covid-easp&#47;covid19&#95;ESP&#47;</a></p><p id="par0080" class="elsevierStylePara elsevierViewall">La <a class="elsevierStyleCrossRef" href="#fig0010">figura 2</a> muestra la evoluci&#243;n de los horizontes &#40;coeficientes <span class="elsevierStyleItalic">a</span> de los modelos&#41; que se fueron calculando diariamente y a lo largo del tiempo&#46; A modo de ejemplo&#44; los modelos predec&#237;an m&#225;s de 900&#46;000 casos de contagio y unas 67&#46;000 muertes en torno al 27 de marzo para el total de Espa&#241;a&#44; y a medida que se sucedieron los d&#237;as estos horizontes estimados descendieron hasta situarse alrededor de 240&#46;000 contagios y 25&#46;000 fallecidos&#46; A partir de los primeros d&#237;as de abril&#44; esas estimaciones permanecen estables a lo largo del tiempo&#46; De manera general se observa que&#44; en todos los casos&#44; al principio el comportamiento de la serie de horizontes era algo err&#225;tica&#44; pero a medida que avanzaron los d&#237;as el par&#225;metro fue estabiliz&#225;ndose&#44; lo cual se puede interpretar como medida de robustez de la estimaci&#243;n del n&#250;mero de contagiados y de fallecidos para cada comunidad aut&#243;noma&#46;</p><elsevierMultimedia ident="fig0010"></elsevierMultimedia><p id="par0085" class="elsevierStylePara elsevierViewall">A partir de las curvas de contagios diarios y de defunciones diarias <span class="elsevierStyleItalic">&#40;g&#40;t&#41;&#41;</span> se hizo una estimaci&#243;n de las fechas en que no se observar&#225;n m&#225;s contagios ni m&#225;s defunciones &#40;<a class="elsevierStyleCrossRef" href="#tbl0005">tabla 1</a>&#41;&#46; Hay que hacer notar que tanto las predicciones de estas fechas como las de los horizontes son orientativas y no ser&#225;n precisas si la situaci&#243;n epidemiol&#243;gica var&#237;a sustancialmente&#46;</p><elsevierMultimedia ident="tbl0005"></elsevierMultimedia></span><span id="sec0020" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0040">Conclusiones</span><p id="par0090" class="elsevierStylePara elsevierViewall">Presentamos en este trabajo una metodolog&#237;a de f&#225;cil uso para modelizar epidemias como la de COVID-19&#46; Consideramos que en esta sencillez radica su fortaleza&#44; ya que se utilizan exclusivamente los datos sobre contagios y defunciones que despu&#233;s se predicen&#44; sin contar con ning&#250;n tipo de covariable externa para su c&#225;lculo&#46; Esto&#44; por una parte&#44; podr&#237;a parecer una debilidad al no a&#241;adir m&#225;s informaci&#243;n a los modelos&#44; pero as&#237; se evita el ruido que podr&#237;an introducir esas hipot&#233;ticas variables externas&#46; Por otra parte&#44; la ausencia de m&#225;s informaci&#243;n hace que la calidad de las predicciones dependa mucho de la calidad de los datos&#46;</p><p id="par0095" class="elsevierStylePara elsevierViewall">Hay que tener en cuenta que las predicciones de los modelos de contagios&#44; sobre todo a partir de aproximadamente la tercera semana de abril de 2020&#44; pueden sufrir grandes variaciones con respecto a los valores observados por los cambios en la definici&#243;n de caso&#46; No ocurre lo mismo con respecto a los modelos de defunciones&#44; que son m&#225;s robustos a lo largo del tiempo al no haber sufrido grandes cambios en su definici&#243;n&#46;</p><p id="par0100" class="elsevierStylePara elsevierViewall">Con respecto a las fechas estimadas del fin de la epidemia en cada comunidad aut&#243;noma&#44; hay que tener en cuenta que son estimaciones aproximadas y que pueden sufrir alteraciones si se producen cambios bruscos en las tendencias&#46; De hecho&#44; los modelos predec&#237;an horizontes de muchos m&#225;s casos y defunciones a finales de marzo que a partir de la segunda quincena de abril&#44; lo que puede deberse a las medidas de confinamiento tomadas por las autoridades&#44; que tienen un efecto en las curvas de la epidemia a partir de al menos una semana desde su implantaci&#243;n<a class="elsevierStyleCrossRef" href="#bib0100"><span class="elsevierStyleSup">10</span></a>&#63;&#46;</p><p id="par0105" class="elsevierStylePara elsevierViewall">En cuanto al fin de la epidemia&#44; las fechas en las que se espera que no haya defunciones son anteriores a las fechas en las que se espera que no haya contagios&#44; y esto tiene mucho sentido dado que no todas las personas contagiadas fallecer&#225;n y que el porcentaje de personas que sobreviven a la enfermedad es mucho mayor que el de las personas que fallecen&#46;</p><p id="par0110" class="elsevierStylePara elsevierViewall">En cualquier caso&#44; en este trabajo presentamos una metodolog&#237;a utilizada para modelizar la epidemia de COVID-19 en Espa&#241;a y en sus comunidades aut&#243;nomas&#44; y el valor que le damos es referente al contexto temporal de la epidemia&#44; aunque somos conscientes de que pasada la crisis esta metodolog&#237;a puede ser matizada&#46;</p></span><span id="sec0025" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0045">Editor responsable del art&#237;culo</span><p id="par0115" class="elsevierStylePara elsevierViewall">Carlos &#193;lvarez Dardet&#46;</p></span><span id="sec0030" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0050">Contribuciones de autor&#237;a</span><p id="par0120" class="elsevierStylePara elsevierViewall">Los dos autores han contribuido a la concepci&#243;n del estudio&#44; la redacci&#243;n del manuscrito y la revisi&#243;n de las distintas versiones&#46; P&#46; S&#225;nchez Villegas realiz&#243; los an&#225;lisis de los datos&#46; Ambos se hacen responsables del contenido &#237;ntegro del trabajo&#46;</p></span><span id="sec0035" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0055">Financiaci&#243;n</span><p id="par0125" class="elsevierStylePara elsevierViewall">Ninguna&#46;</p></span><span id="sec0040" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0060">Conflicto de intereses</span><p id="par0130" class="elsevierStylePara elsevierViewall">Ninguno&#46;</p></span></span>"
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        "resumen" => "<span id="abst0005" class="elsevierStyleSection elsevierViewall"><p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">Durante la crisis de salud internacional provocada por la pandemia de COVID-19&#44; adem&#225;s de conocer los datos sobre contagios&#44; muertes y ocupaci&#243;n de camas hospitalarias tambi&#233;n es necesario hacer predicciones que ayuden a la gesti&#243;n de la crisis por parte de las autoridades sanitarias&#46; El presente trabajo tiene como objetivo describir la metodolog&#237;a utilizada para la elaboraci&#243;n de modelos predictivos de contagios y defunciones para la epidemia de COVID-19 en Espa&#241;a basados en curvas de Gompertz&#46; La metodolog&#237;a se aplica al total del pa&#237;s y a cada una de sus comunidades aut&#243;nomas&#46; De acuerdo con los datos oficiales publicados a la fecha de realizaci&#243;n de este trabajo&#44; y a trav&#233;s de los modelos descritos&#44; estimamos un total de alrededor de 240&#46;000 contagiados y 25&#46;000 fallecidos al final de la epidemia&#46; Pronosticamos el final de la epidemia entre los meses de junio y julio de 2020&#46;</p></span>"
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        "resumen" => "<span id="abst0010" class="elsevierStyleSection elsevierViewall"><p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">During the international health crisis caused by the COVID-19 pandemic&#44; it is necessary not only to know the data on infections&#44; deaths and the occupation of hospital beds&#44; but also to make predictions that help health authorities in the management of the crisis&#46; The present work aims to describe the methodology used to develop predictive models of infections and deaths for the COVID-19 epidemic in Spain&#44; based on Gompertz curves&#46; The methodology is applied to the country as a whole and to each of its Autonomous Communities&#46; Based on the official data available on the date of this work&#44; and through the models described&#44; we estimate a total of around 240&#46;000 infected and 25&#46;000 deaths at the end of the epidemic&#46; At a national level&#44; we forecast the end of the epidemic between June and July 2020&#46;</p></span>"
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                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2727&#46;282 &#40;2628&#46;178&#44;2826&#46;386&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">25&#46;458 &#40;24&#46;83&#44;26&#46;086&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t\ttop\n
                  \t\t\t\t">09&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;061 &#40;-0&#46;066&#44;-0&#46;056&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">351&#46;555 &#40;319&#46;567&#44;383&#46;542&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">38&#46;859 &#40;37&#46;219&#44;40&#46;5&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">05&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Baleares&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;116 &#40;-0&#46;124&#44;-0&#46;107&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">1828&#46;794 &#40;1779&#46;225&#44;1878&#46;363&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">23&#46;256 &#40;22&#46;857&#44;23&#46;654&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">15&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;075 &#40;-0&#46;083&#44;-0&#46;067&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">223&#46;425 &#40;203&#46;344&#44;243&#46;506&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">34&#46;923 &#40;33&#46;49&#44;36&#46;356&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">18&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Canarias&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;121 &#40;-0&#46;126&#44;-0&#46;116&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2169&#46;584 &#40;2139&#46;665&#44;2199&#46;502&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">22&#46;922 &#40;22&#46;719&#44;23&#46;126&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">14&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;123 &#40;-0&#46;135&#44;-0&#46;112&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">123&#46;78 &#40;119&#46;256&#44;128&#46;304&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">26&#46;745 &#40;26&#46;271&#44;27&#46;22&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">23&#47;04&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Cantabria&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;113 &#40;-0&#46;125&#44;-0&#46;102&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2140&#46;596 &#40;2056&#46;683&#44;2224&#46;509&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">24&#46;561 &#40;24&#46;002&#44;25&#46;12&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">18&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;081 &#40;-0&#46;089&#44;-0&#46;074&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">219&#46;775 &#40;203&#46;95&#44;235&#46;599&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">34&#46;6 &#40;33&#46;519&#44;35&#46;681&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">16&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Castilla-La Mancha&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;088 &#40;-0&#46;092&#44;-0&#46;085&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">20389&#46;014 &#40;19938&#46;915&#44;20839&#46;113&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">29&#46;434 &#40;29&#46;107&#44;29&#46;762&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">29&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;083 &#40;-0&#46;086&#44;-0&#46;079&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">2619&#46;466 &#40;2538&#46;272&#44;2700&#46;66&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">31&#46;887 &#40;31&#46;413&#44;32&#46;362&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">12&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Castilla y Le&#243;n&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;069 &#40;-0&#46;073&#44;-0&#46;064&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">22078&#46;697 &#40;20977&#46;38&#44;23180&#46;014&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">31&#46;945 &#40;31&#46;061&#44;32&#46;829&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">24&#47;07&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;107 &#40;-0&#46;109&#44;-0&#46;105&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">1715&#46;048 &#40;1698&#46;215&#44;1731&#46;88&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">29&#46;785 &#40;29&#46;657&#44;29&#46;914&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">24&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Catalu&#241;a&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
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                  \t\t\t\t">-0&#46;086 &#40;-0&#46;09&#44;-0&#46;081&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">49227&#46;704 &#40;47679&#46;816&#44;50775&#46;591&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">27&#46;969 &#40;27&#46;476&#44;28&#46;462&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">10&#47;07&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;129 &#40;-0&#46;134&#44;-0&#46;123&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">4313&#46;684 &#40;4238&#46;415&#44;4388&#46;953&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">27&#46;729 &#40;27&#46;507&#44;27&#46;95&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">22&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Ceuta&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">-0&#46;157 &#40;-0&#46;183&#44;-0&#46;131&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">115&#46;651 &#40;109&#46;642&#44;121&#46;66&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t  " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">28&#46;416 &#40;27&#46;846&#44;28&#46;987&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">-0&#46;262 &#40;-0&#46;393&#44;-0&#46;131&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">30&#46;558 &#40;29&#46;353&#44;31&#46;763&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">C&#46; Valenciana&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;099 &#40;-0&#46;105&#44;-0&#46;094&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">11321&#46;285 &#40;11039&#46;421&#44;11603&#46;15&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">25&#46;324 &#40;24&#46;954&#44;25&#46;694&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;095 &#40;-0&#46;099&#44;-0&#46;091&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">1295&#46;589 &#40;1265&#46;824&#44;1325&#46;353&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">30&#46;546 &#40;30&#46;225&#44;30&#46;867&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">27&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Extremadura&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;085 &#40;-0&#46;095&#44;-0&#46;074&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">3688&#46;372 &#40;3434&#46;953&#44;3941&#46;79&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;766 &#40;25&#46;66&#44;27&#46;873&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;107 &#40;-0&#46;113&#44;-0&#46;102&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">446&#46;697 &#40;434&#46;893&#44;458&#46;501&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">29&#46;8 &#40;29&#46;454&#44;30&#46;146&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">11&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Galicia&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;118 &#40;-0&#46;123&#44;-0&#46;113&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">8960&#46;746 &#40;8820&#46;319&#44;9101&#46;173&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;091 &#40;25&#46;881&#44;26&#46;302&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;102 &#40;-0&#46;106&#44;-0&#46;097&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">429&#46;271 &#40;418&#46;027&#44;440&#46;516&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">32&#46;36 &#40;32&#46;024&#44;32&#46;697&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">15&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Madrid&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;079 &#40;-0&#46;085&#44;-0&#46;074&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">67301&#46;118 &#40;64827&#46;97&#44;69774&#46;266&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;79 &#40;26&#46;183&#44;27&#46;397&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;098 &#40;-0&#46;101&#44;-0&#46;096&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">8196&#46;958 &#40;8097&#46;911&#44;8296&#46;005&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">26&#46;119 &#40;25&#46;941&#44;26&#46;297&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">09&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
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                  \t\t\t\t">Melilla&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;086 &#40;-0&#46;095&#44;-0&#46;077&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">125&#46;585 &#40;119&#46;102&#44;132&#46;067&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">24&#46;356 &#40;23&#46;502&#44;25&#46;211&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;23 &#40;-0&#46;282&#44;-0&#46;177&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">2&#46;059 &#40;1&#46;949&#44;2&#46;17&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">24&#46;6 &#40;23&#46;781&#44;25&#46;42&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">13&#47;04&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Murcia&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;111 &#40;-0&#46;119&#44;-0&#46;103&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">1753&#46;878 &#40;1707&#46;227&#44;1800&#46;529&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">23&#46;685 &#40;23&#46;296&#44;24&#46;073&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">16&#47;05&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;132 &#40;-0&#46;14&#44;-0&#46;125&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">131&#46;682 &#40;128&#46;555&#44;134&#46;809&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
                  \t\t\t\t\ttable-entry\n
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                  \t\t\t\t">30&#46;778 &#40;30&#46;505&#44;31&#46;051&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">27&#47;04&#47;20&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td></tr><tr title="table-row"><td class="td-with-role" title="\n
                  \t\t\t\t\ttable-entry\n
                  \t\t\t\t ; entry_with_role_rowhead " align="left" valign="\n
                  \t\t\t\t\ttop\n
                  \t\t\t\t">Navarra&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">-0&#46;083 &#40;-0&#46;087&#44;-0&#46;08&#41;&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">5570&#46;162 &#40;5450&#46;229&#44;5690&#46;095&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">26&#46;716 &#40;26&#46;369&#44;27&#46;063&#41;&nbsp;\t\t\t\t\t\t\n
                  \t\t\t\t</td><td class="td" title="\n
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                  \t\t\t\t">15&#47;06&#47;20&nbsp;\t\t\t\t\t\t\n
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                  \t\t\t\t">-0&#46;054 &#40;-0&#46;068&#44;-0&#46;04&#41;&nbsp;\t\t\t\t\t\t\n
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Article information
ISSN: 02139111
Original language: Spanish
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2022 March 272 73 345
2022 February 258 55 313
2022 January 272 91 363
2021 December 315 89 404
2021 November 524 127 651
2021 October 310 164 474
2021 September 138 83 221
2021 August 145 84 229
2021 July 188 108 296
2021 June 241 101 342
2021 May 254 140 394
2021 April 385 331 716
2021 March 201 74 275
2021 February 131 31 162
2021 January 152 40 192
2020 December 147 56 203
2020 November 128 28 156
2020 October 132 41 173
2020 September 226 56 282
2020 August 280 60 340
2020 July 494 123 617
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¿Es usted profesional sanitario apto para prescribir o dispensar medicamentos?

Are you a health professional able to prescribe or dispense drugs?