<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332021000100055</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v28i1.42077</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Optimizing the quarantine cost for suppression of the COVID-19 epidemic in México]]></article-title>
<article-title xml:lang="es"><![CDATA[Optimización del costo de la cuarentena para la supresión de la epidemia del COVID-19 en México]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Choque-Rivero]]></surname>
<given-names><![CDATA[Abdon E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Khailov]]></surname>
<given-names><![CDATA[Evgenii N.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Grigorieva]]></surname>
<given-names><![CDATA[Ellina V.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Michoacana de San Nicolás de Hidalgo  Institute of Physics and Mathematics]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Lomonosov Moscow State University Faculty of Computational Mathematics and Cybernetics ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Russia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Texas Woman&#8217;s University  Department of Mathematics and Computer Sciences]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>USA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<volume>28</volume>
<numero>1</numero>
<fpage>55</fpage>
<lpage>78</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332021000100055&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332021000100055&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332021000100055&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This paper is one of the few attempts to use the optimal control theory to find optimal quarantine strategies for eradication of the spread of the COVID-19 infection in the Mexican human population. This is achieved by introducing into the SEIR model a bounded control function of time that reflects these quarantine measures. The objective function to be minimized is the weighted sum of the total infection level in the population and the total cost of the quarantine. An optimal control problem reflecting the search for an effective quarantine strategy is stated and solved analytically and numerically. The properties of the corresponding optimal control are established analytically by applying the Pontryagin maximum principle. The optimal solution is obtained numerically by solving the two-point boundary value problem for the maximum principle using MATLAB software. A detailed discussion of the results and the corresponding practical conclusions are presented.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este trabajo empleamos la teoría de control óptimo para encontrar una cuarentena óptima y estrategias para la erradicación de la propagación de la infección por COVID-19 en la población humana mexicana. En un modelo SEIR, introducimos un control acotado que es una función respecto del tiempo, la cual refleja las medidas de la cuarentena. La función objetivo a minimizar es la suma ponderada del nivel total de infección en la población y el costo total de la cuarentena. Planteamos un problema de control óptimo que representa la búsqueda de una estrategia eficaz de una cuarentena. Resolvemos este problema analíticamente y numéricamente. Establecemos analíticamente las propiedades del control óptimo correspondiente aplicando el principio del máximo de Pontryagin. La solución óptima se obtiene resolviendo un problema de valor de frontera de dos puntos asociado al principio del máximo. Usamos el software MATLAB. Presentamos una discusión detallada de los resultados y las correspondientes conclusiones prácticas.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[coronavirus]]></kwd>
<kwd lng="en"><![CDATA[quarantine cost]]></kwd>
<kwd lng="en"><![CDATA[Pontryagin maximum principal]]></kwd>
<kwd lng="en"><![CDATA[optimal control.]]></kwd>
<kwd lng="es"><![CDATA[coronavirus]]></kwd>
<kwd lng="es"><![CDATA[costo de una cuarentena]]></kwd>
<kwd lng="es"><![CDATA[principio del máximo de Pontryagin]]></kwd>
<kwd lng="es"><![CDATA[control óptimo.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[I,H]]></surname>
<given-names><![CDATA[Aslan]]></given-names>
</name>
<name>
<surname><![CDATA[M]]></surname>
<given-names><![CDATA[Demir]]></given-names>
</name>
<name>
<surname><![CDATA[M,M]]></surname>
<given-names><![CDATA[Wise]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Lenhart.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modeling COVID-19: forecasting and analyzing the dynamics of the outbreak in Hubei and Turkey]]></article-title>
<source><![CDATA[MedRxiv]]></source>
<year>2020</year>
<page-range>1-17</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[F]]></surname>
<given-names><![CDATA[Brauer]]></given-names>
</name>
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Castillo-Chavez.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Models in Population Biology and Epidemiology]]></source>
<year>2012</year>
<publisher-loc><![CDATA[ew York-Heidelberg-Dordrecht-London ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Cao]]></given-names>
</name>
<name>
<surname><![CDATA[Q]]></surname>
<given-names><![CDATA[Zhang]]></given-names>
</name>
<name>
<surname><![CDATA[X]]></surname>
<given-names><![CDATA[Lu]]></given-names>
</name>
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Pfeiffer]]></given-names>
</name>
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Jia]]></given-names>
</name>
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Song]]></given-names>
</name>
<name>
<surname><![CDATA[D,D]]></surname>
<given-names><![CDATA[Zeng.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estimating the effective reproduction number of the 2019-nCoV in China]]></article-title>
<source><![CDATA[MedRxiv]]></source>
<year>2020</year>
<page-range>1-8</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[T,-M]]></surname>
<given-names><![CDATA[Chen]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Rui]]></given-names>
</name>
<name>
<surname><![CDATA[Q,-P]]></surname>
<given-names><![CDATA[Wang]]></given-names>
</name>
<name>
<surname><![CDATA[Z,-Y]]></surname>
<given-names><![CDATA[Zhao]]></given-names>
</name>
<name>
<surname><![CDATA[J,-A]]></surname>
<given-names><![CDATA[Cui]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Yin.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A mathematical model for simulating the phase-based transmissibility of a novel coronavirus]]></article-title>
<source><![CDATA[Infect. Dis. Poverty.]]></source>
<year>2020</year>
<volume>9</volume>
<numero>24</numero>
<issue>24</issue>
<page-range>1-8</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[W,H]]></surname>
<given-names><![CDATA[Fleming]]></given-names>
</name>
<name>
<surname><![CDATA[R,W]]></surname>
<given-names><![CDATA[Rishel.]]></given-names>
</name>
</person-group>
<source><![CDATA[Deterministic and Stochastic Optimal Control]]></source>
<year>1975</year>
<publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Gaff]]></given-names>
</name>
<name>
<surname><![CDATA[E]]></surname>
<given-names><![CDATA[Schaefer.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal control applied to vaccination and treatment strategies for various epidemiological models]]></article-title>
<source><![CDATA[Math. Biosci. Eng.]]></source>
<year>2009</year>
<volume>6</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>469-92</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="">
<collab>Gobierno de la Ciudad de México.</collab>
<source><![CDATA[El modelo epidemiológico del Gobierno de la Ciudad de México]]></source>
<year>2020</year>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="">
<collab>Gobierno de México.</collab>
<source><![CDATA[Proyecciones de la población de México y de las entidades federativas, 2016-2050]]></source>
<year>2019</year>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="">
<collab>Gobierno de México.</collab>
<source><![CDATA[Indicadores demográficos de México de 1950 a 2050]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="">
<collab>Gobierno de México.</collab>
<source><![CDATA[Aviso epidemiológico - Casos de infección respiratoria asociados a Coronavirus (COVID-19)]]></source>
<year>2020</year>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E,V]]></surname>
<given-names><![CDATA[Grigorieva]]></given-names>
</name>
<name>
<surname><![CDATA[E,N]]></surname>
<given-names><![CDATA[Khailov.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal intervention strategies for a SEIR control model of Ebola epidemics]]></article-title>
<source><![CDATA[Mathematics]]></source>
<year>2015</year>
<volume>3</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>961-83</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E,V]]></surname>
<given-names><![CDATA[Grigorieva]]></given-names>
</name>
<name>
<surname><![CDATA[E,N]]></surname>
<given-names><![CDATA[Khailov.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estimating the number of switchings of the optimal interventions strategies for SEIR control models of Ebola epidemics]]></article-title>
<source><![CDATA[Pure and Applied Functional Analysis]]></source>
<year>2016</year>
<volume>1</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>541-72</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E,V]]></surname>
<given-names><![CDATA[Grigorieva]]></given-names>
</name>
<name>
<surname><![CDATA[P,B]]></surname>
<given-names><![CDATA[Deignan]]></given-names>
</name>
<name>
<surname><![CDATA[E,N]]></surname>
<given-names><![CDATA[Khailov.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal control problem for a SEIR type model of Ebola epidemics]]></article-title>
<source><![CDATA[Revista de Matemática: Teoría y Aplicaciones]]></source>
<year>2017</year>
<volume>24</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>79-96</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E,V]]></surname>
<given-names><![CDATA[Grigorieva]]></given-names>
</name>
<name>
<surname><![CDATA[E,N]]></surname>
<given-names><![CDATA[Khailov.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal preventive strategies for SEIR type model of the 2014 Ebola epidemics]]></article-title>
<source><![CDATA[Dyn. Contin. Discrete Impuls. Syst.]]></source>
<year>2017</year>
<volume>24</volume>
<page-range>155-82</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E,V]]></surname>
<given-names><![CDATA[Grigorieva]]></given-names>
</name>
<name>
<surname><![CDATA[E,N]]></surname>
<given-names><![CDATA[Khailov.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Determination of the optimal controls for an Ebola epidemic model]]></article-title>
<source><![CDATA[Discrete Cont. Dyn. Syst.]]></source>
<year>2018</year>
<volume>11</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1071-101</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Jia]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Ding]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Liu]]></given-names>
</name>
<name>
<surname><![CDATA[G]]></surname>
<given-names><![CDATA[Liao]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Li]]></given-names>
</name>
<name>
<surname><![CDATA[B]]></surname>
<given-names><![CDATA[Duan]]></given-names>
</name>
<name>
<surname><![CDATA[G]]></surname>
<given-names><![CDATA[Wang]]></given-names>
</name>
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Zhang.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modeling the control of COVID-19: impact of policy interventions and meteorological factors]]></article-title>
<source><![CDATA[Electron J. Differ. Eq.]]></source>
<year>2020</year>
<volume>23</volume>
<page-range>1-24</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Jing]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Minghui]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Gang]]></given-names>
</name>
<name>
<surname><![CDATA[Z,K]]></surname>
<given-names><![CDATA[Lu.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Monitoring transmissibility and mortality of COVID-19 in Europe]]></article-title>
<source><![CDATA[Int. J. Infect. Dis.]]></source>
<year>2020</year>
<page-range>1-16</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E]]></surname>
<given-names><![CDATA[Jung]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Lenhart]]></given-names>
</name>
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Feng.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal control of treatments in a twostrain tuberculosis model]]></article-title>
<source><![CDATA[Discrete Cont. Dyn. Syst.]]></source>
<year>2002</year>
<volume>2</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>473-82</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[U]]></surname>
<given-names><![CDATA[Ledzewicz]]></given-names>
</name>
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Schättler.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On optimal singular controls for a general SIR-model with vaccination and treatment]]></article-title>
<source><![CDATA[Discrete Cont. Dyn. Syst.]]></source>
<year>2011</year>
<page-range>981-90</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[E,B]]></surname>
<given-names><![CDATA[Lee]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Marcus.]]></given-names>
</name>
</person-group>
<source><![CDATA[Foundations of Optimal Control Theory]]></source>
<year>1967</year>
<publisher-loc><![CDATA[New York NY, USA ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Liu]]></given-names>
</name>
<name>
<surname><![CDATA[A,A]]></surname>
<given-names><![CDATA[Gayle]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Wilder-Smith]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Rocklöv.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The reproductive number of COVID-19 is higher compared to SARS coronavirus]]></article-title>
<source><![CDATA[J. Travel Med.]]></source>
<year>2020</year>
<page-range>1-4</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Liu]]></given-names>
</name>
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Magal]]></given-names>
</name>
<name>
<surname><![CDATA[O]]></surname>
<given-names><![CDATA[Seydi]]></given-names>
</name>
<name>
<surname><![CDATA[G]]></surname>
<given-names><![CDATA[Webb.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Understanding unreported cases in the COVID-19 epidemic outbreak in Wuhan, China, and the importance of major public health interventions]]></article-title>
<source><![CDATA[Biology]]></source>
<year>2020</year>
<volume>9</volume>
<numero>50</numero>
<issue>50</issue>
<page-range>1-12</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J,P]]></surname>
<given-names><![CDATA[Mateus]]></given-names>
</name>
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Rebelo]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Rosa]]></given-names>
</name>
<name>
<surname><![CDATA[C,M]]></surname>
<given-names><![CDATA[Silva]]></given-names>
</name>
<name>
<surname><![CDATA[D,F,M]]></surname>
<given-names><![CDATA[Torres.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal control of non-autonomous SEIRS models with vaccination and treatment]]></article-title>
<source><![CDATA[Discrete Cont. Dyn. Syst.]]></source>
<year>2018</year>
<volume>11</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1179-99</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[M]]></surname>
<given-names><![CDATA[Park]]></given-names>
</name>
<name>
<surname><![CDATA[A,R]]></surname>
<given-names><![CDATA[Cook]]></given-names>
</name>
<name>
<surname><![CDATA[J,T]]></surname>
<given-names><![CDATA[Lim]]></given-names>
</name>
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Sun]]></given-names>
</name>
<name>
<surname><![CDATA[B,L]]></surname>
<given-names><![CDATA[Dickens.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A systematic review of COVID-19 epidemiology based on current evidence]]></article-title>
<source><![CDATA[J. Clin. Med.]]></source>
<year>2020</year>
<volume>9</volume>
<numero>967</numero>
<issue>967</issue>
<page-range>1-13</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[L,S]]></surname>
<given-names><![CDATA[Pontryagin]]></given-names>
</name>
<name>
<surname><![CDATA[V,G]]></surname>
<given-names><![CDATA[Boltyanskii]]></given-names>
</name>
<name>
<surname><![CDATA[R,V]]></surname>
<given-names><![CDATA[Gamkrelidze]]></given-names>
</name>
<name>
<surname><![CDATA[E,F]]></surname>
<given-names><![CDATA[Mishchenko.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Theory of Optimal Processes]]></source>
<year>1962</year>
<publisher-loc><![CDATA[New York NY, USA, ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[F]]></surname>
<given-names><![CDATA[Saldaña]]></given-names>
</name>
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Flores-Arguedas]]></given-names>
</name>
<name>
<surname><![CDATA[J,A]]></surname>
<given-names><![CDATA[Camacho-Gutiérrez]]></given-names>
</name>
<name>
<surname><![CDATA[I]]></surname>
<given-names><![CDATA[Barrandas.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Modeling the transmission dynamics and the impact of the control interventions for the COVID-19 epidemic outbreak]]></article-title>
<source><![CDATA[Math. Biosci. Eng.]]></source>
<year>2020</year>
</nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Schättler]]></given-names>
</name>
<name>
<surname><![CDATA[U]]></surname>
<given-names><![CDATA[Ledzewicz.]]></given-names>
</name>
</person-group>
<source><![CDATA[Optimal Control for Mathematical Models of Cancer Therapies: An Application of Geometric Methods]]></source>
<year>2015</year>
<publisher-loc><![CDATA[New York-Heidelberg-Dordrecht-London ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[C,J]]></surname>
<given-names><![CDATA[Silva]]></given-names>
</name>
<name>
<surname><![CDATA[D,F,M]]></surname>
<given-names><![CDATA[Torres.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Optimal control for a tuberculosis model with reinfection and post-exposure interventions]]></article-title>
<source><![CDATA[Math. Biosci.]]></source>
<year>2013</year>
<volume>244</volume>
<page-range>153-1164</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Smith?]]></given-names>
</name>
</person-group>
<source><![CDATA[Modelling Disease Ecology with Mathematics]]></source>
<year>2008</year>
<publisher-loc><![CDATA[USA ]]></publisher-loc>
<publisher-name><![CDATA[Springfield MO]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[B]]></surname>
<given-names><![CDATA[Tang]]></given-names>
</name>
<name>
<surname><![CDATA[X]]></surname>
<given-names><![CDATA[Wang]]></given-names>
</name>
<name>
<surname><![CDATA[Q]]></surname>
<given-names><![CDATA[Li]]></given-names>
</name>
<name>
<surname><![CDATA[N,L]]></surname>
<given-names><![CDATA[Bragazzi]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Tang]]></given-names>
</name>
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Xiao]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Wu.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions]]></article-title>
<source><![CDATA[J. Clin. Med.]]></source>
<year>2020</year>
<volume>9</volume>
<numero>462</numero>
<issue>462</issue>
<page-range>1-13</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[van den Driessche]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Watmough.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission]]></article-title>
<source><![CDATA[Math. Biosci.]]></source>
<year>2002</year>
<volume>180</volume>
<page-range>29-48</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="">
<collab>World Health Organization.</collab>
<source><![CDATA[Coronavirus disease (COVID-2019) situation reports]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wu]]></surname>
<given-names><![CDATA[J,T,]]></given-names>
</name>
<name>
<surname><![CDATA[Leung]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
<name>
<surname><![CDATA[Leung]]></surname>
<given-names><![CDATA[G,M,]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study]]></article-title>
<source><![CDATA[Lancet]]></source>
<year>2020</year>
<volume>395</volume>
<numero>10225</numero>
<issue>10225</issue>
<page-range>689-97</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhao]]></surname>
<given-names><![CDATA[S,]]></given-names>
</name>
<name>
<surname><![CDATA[Lin]]></surname>
<given-names><![CDATA[Q,]]></given-names>
</name>
<name>
<surname><![CDATA[Ran]]></surname>
<given-names><![CDATA[J,]]></given-names>
</name>
<name>
<surname><![CDATA[Musa]]></surname>
<given-names><![CDATA[S,S,]]></given-names>
</name>
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[G,]]></given-names>
</name>
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[W,]]></given-names>
</name>
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[M,H,]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak]]></article-title>
<source><![CDATA[Int. J. Infect. Dis.]]></source>
<year>2020</year>
<volume>92</volume>
<page-range>214-7</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Z]]></surname>
<given-names><![CDATA[Zhuang]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Zhao]]></given-names>
</name>
<name>
<surname><![CDATA[Q]]></surname>
<given-names><![CDATA[Lin]]></given-names>
</name>
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Cao]]></given-names>
</name>
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Lou]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Yang]]></given-names>
</name>
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[He.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Preliminary estimation of the novel coronavirus disease (COVID-19) cases in Iran: A modelling analysis based on overseas cases and air travel data]]></article-title>
<source><![CDATA[Int. J. Infect. Dis.]]></source>
<year>2020</year>
<volume>94</volume>
<page-range>29-31</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
