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    <language>eng</language>
    <pageFirst/>
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    <pageNumber>154</pageNumber>
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    <issue/>
    <volume/>
    <type>doctoralthesis</type>
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    <completedDate>2013-11-06</completedDate>
    <publishedDate>2013-11-06</publishedDate>
    <thesisDateAccepted>2013-09-12</thesisDateAccepted>
    <title language="eng">A Mathematical Tuberculosis Model in Cameroon</title>
    <abstract language="eng">This thesis firstly presents a nonlinear extended deterministic model for the transmission dynamics of tuberculosis, based on realistic assumptions and data collected from the WHO. This model enables a comprehensive qualitative analysis of various aspects in the outbreak and control of tuberculosis in Sub-Saharan Africa countries and successfully reproduces the epidemiology of tuberculosis in Cameroon for the past (from 1994-2010). Some particular properties of the model and its solution have been presented using the comparison theorem applied to the theory of differential equations. The existence and the stability of a disease free equilibrium has been discussed using the Perron-Frobenius theorem and Metzler stable matrices. &#13;
Furthermore, we computed the basic reproduction number, i.e. the number of cases that one case generates on average over the course of its infectious period. Rigorous qualitative analysis of the model reveals that, in contrast to the model without reinfections, the full model with reinfection exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with a stable endemic equilibrium when a certain threshold quantity, known as the basic reproduction ratio (R0), is less than unity. The global stability of the disease-free equilibrium has been discussed using the concepts of Lyapunov stability and bifurcation theory.&#13;
With the help of a sensitivity analysis using data of Cameroon, we identified the relevant parameters which play a key role for the transmission and the control of the disease. This was possible applying sophisticated numerical methods (POEM) developed at ZIB. Using advanced approaches for optimal control considering the costs for chemoprophylaxis, treatment and educational campaigns should provide a framework for designing realistic cost effective strategies with different intervention methods. The forward-backward sweep method has been used to solve the numerical optimal control problem. The numerical result of the optimal control problem reveals that combined effort in education and chemoprophylaxis may lead to a reduction of 80\% in the number of infected people in 10 years.&#13;
The mathematical and numerical approaches developed in this thesis could be similarly applied in many other Sub-Saharan countries where TB is a public health problem.</abstract>
    <identifier type="url">http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000095327</identifier>
    <identifier type="urn">urn:nbn:de:kobv:188-fudissthesis000000095327-7</identifier>
    <advisor>Peter Deuflhard</advisor>
    <author>Dany Pascal Moualeu-Ngangue</author>
    <submitter>Dany Pascal Moualeu-Ngangue</submitter>
    <collection role="ccs" number="I.">Computing Methodologies</collection>
    <collection role="pacs" number="80.00.00">INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY</collection>
    <collection role="msc" number="34-XX">ORDINARY DIFFERENTIAL EQUATIONS</collection>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="collections" number="">Dissertationen</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="projects" number="TBmod">TBmod</collection>
    <thesisPublisher>Freie Universität Berlin</thesisPublisher>
    <thesisGrantor>Freie Universität Berlin</thesisGrantor>
  </doc>
  <doc>
    <id>4308</id>
    <completedYear/>
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    <language>eng</language>
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    <completedDate>2013-11-14</completedDate>
    <publishedDate>2013-11-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Parameter Identification for a Tuberculosis Model in Cameroon</title>
    <abstract language="eng">A  deterministic model of tuberculosis in  sub-Saharan Africa in general and Cameroon in particular including lack of access to the treatment and weak diagnose capacity is designed and analyzed  with respect to its transmission dynamics.&#13;
The model includes both  frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are  non-negative.&#13;
A sensitivity analysis of model parameters is performed and most sensitive   parameters of the model are identified using a state-of-the-art Gauss-Newton&#13;
Method. In particular,  parameters representing the proportion of individuals having access to medical facilities have a large impact on the dynamics of the disease.  It has been shown that an increase of these parameter values over the&#13;
 time can significantly reduce the disease burden in the population within the next 15 years.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-43087</identifier>
    <identifier type="doi">10.1371/journal.pone.0120607</identifier>
    <enrichment key="SourceTitle">Appeared in: PLOS ONE Published: April 13, 2015</enrichment>
    <submitter>Dany Pascal Moualeu-Ngangue</submitter>
    <author>Dany Pascal Moualeu-Ngangue</author>
    <author>Susanna Röblitz</author>
    <author>Rainald Ehrig</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-72</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Tuberculosis,  parameter identification, sensitivity analysis, Gauss-Newton method, Nonlinear dynamical systems.</value>
    </subject>
    <collection role="msc" number="34-XX">ORDINARY DIFFERENTIAL EQUATIONS</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="projects" number="TBmod">TBmod</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4308/ZIBReport-13-72.pdf</file>
  </doc>
  <doc>
    <id>4314</id>
    <completedYear/>
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    <language>eng</language>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-11-25</completedDate>
    <publishedDate>2013-11-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal control for a tuberculosis model with undetected cases in Cameroon</title>
    <abstract language="eng">This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A  mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population,  Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods.  It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-43142</identifier>
    <enrichment key="SourceTitle">published  in Comm. Nonlin. Sci. Num. Sim. 20 (3): 986-1003, 2014.</enrichment>
    <submitter>Dany Pascal Moualeu-Ngangue</submitter>
    <author>Dany Pascal Moualeu-Ngangue</author>
    <author>Martin Weiser</author>
    <author>Rainald Ehrig</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-73</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Tuberculosis</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Nonlinear dynamical systems</value>
    </subject>
    <collection role="msc" number="34-XX">ORDINARY DIFFERENTIAL EQUATIONS</collection>
    <collection role="msc" number="49-XX">CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]</collection>
    <collection role="msc" number="65-XX">NUMERICAL ANALYSIS</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="ehrig">Ehrig, Rainald</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="TBmod">TBmod</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4314/Optimal_ControlZIB1373.pdf</file>
  </doc>
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    <id>5457</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
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    <completedDate>--</completedDate>
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    <title language="eng">Parameter Identification in a Tuberculosis Model for Cameroon</title>
    <abstract language="eng">A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.</abstract>
    <parentTitle language="eng">PLOS ONE</parentTitle>
    <identifier type="doi">10.1371/journal.pone.0120607</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-43087</enrichment>
    <author>Dany Pascal Moualeu-Ngangue</author>
    <submitter>Regine Kossick</submitter>
    <author>Susanna Röblitz</author>
    <author>Rainald Ehrig</author>
    <author>Peter Deuflhard</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
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    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
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    <id>5436</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
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    <title language="eng">Parameter Estimation of a Tuberculosis Model in a Patchy Environment: Case of Cameroon</title>
    <parentTitle language="eng">BIOMAT - Proceedings of the 12th International Symposium on Mathematical and Computational Biology, Toronto, 2013</parentTitle>
    <identifier type="doi">10.1142/9789814602228_0021</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Dany Pascal Moualeu-Ngangue</author>
    <submitter> Stötzel</submitter>
    <author>Samuel Bowong</author>
    <author>Jürgen Kurths</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
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    <collection role="projects" number="TBmod">TBmod</collection>
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    <language>eng</language>
    <pageFirst>986</pageFirst>
    <pageLast>1003</pageLast>
    <pageNumber>18</pageNumber>
    <edition/>
    <issue>3</issue>
    <volume>20</volume>
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    <title language="eng">Optimal control for a tuberculosis model with undetected cases in Cameroon</title>
    <abstract language="eng">This paper considers the optimal control of tuberculosis through education, diagnosis campaign and chemoprophylaxis of latently infected. A  mathematical model which includes important components such as undiagnosed infectious, diagnosed infectious, latently infected and lost-sight infectious is formulated. The model combines a frequency dependent and a density dependent force of infection for TB transmission. Through optimal control theory and numerical simulations, a cost-effective balance of two different intervention methods is obtained. Seeking to minimize the amount of money the government spends when tuberculosis remain endemic in the Cameroonian population,  Pontryagin's maximum principle is used to characterize the optimal control. The optimality system is derived and solved numerically using the forward-backward sweep method (FBSM). Results provide a framework for designing cost-effective strategies for diseases with multiple intervention methods.  It comes out that combining chemoprophylaxis and education, the burden of TB can be reduced by 80 % in 10 years.</abstract>
    <parentTitle language="eng">Communications in Nonlinear Science and Numerical Simulation</parentTitle>
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