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  <doc>
    <id>4195</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2013-08-07</completedDate>
    <publishedDate>2013-08-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Markov Control Processes with Rare State Observation: Theory and Application to Treatment Scheduling in HIV-1</title>
    <abstract language="eng">Markov Decision Processes (MDP) or Partially Observable MDPs (POMDP) are&#13;
used for modelling situations in which the evolution of a process is partly random and&#13;
partly controllable. These MDP theories allow for computing the optimal control policy&#13;
for processes that can continuously or frequently be observed, even if only partially.&#13;
However, they cannot be applied if state observation is very costly and therefore rare&#13;
(in time). We present a novel MDP theory for rare, costly observations and derive the&#13;
corresponding Bellman equation. In the new theory, state information can be derived&#13;
for a particular cost after certain, rather long time intervals. The resulting information&#13;
costs enter into the total cost and thus into the optimization criterion. This approach&#13;
applies to many real world problems, particularly in the medical context, where the&#13;
medical condition is examined rather rarely because examination costs are high. At the&#13;
same time, the approach allows for efficient numerical realization. We demonstrate the&#13;
usefulness of the novel theory by determining, from the national economic perspective,&#13;
optimal therapeutic policies for the treatment of the human immunodefficiency virus&#13;
(HIV) in resource-rich and resource-poor settings. Based on the developed theory and&#13;
models, we discover that available drugs may not be utilized efficiently in resource-poor&#13;
settings due to exorbitant diagnostic costs.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-41955</identifier>
    <identifier type="doi">10.4310/CMS.2014.v12.n5.a4</identifier>
    <enrichment key="SourceTitle">Appeared In: Comm. in Mathematical Sciences 12 (2014) 859-877</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <author>Max von Kleist</author>
    <series>
      <title>ZIB-Report</title>
      <number>13-34</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>information costs</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>hidden state</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bellmann equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal therapeutic policies</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>diagnostic frequency</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>resource-poor</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>resource-rich</value>
    </subject>
    <collection role="msc" number="49N30">Problems with incomplete information [See also 93C41]</collection>
    <collection role="msc" number="60J27">Continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="60J28">Applications of continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="90C40">Markov and semi-Markov decision processes</collection>
    <collection role="msc" number="93B07">Observability</collection>
    <collection role="msc" number="93E20">Optimal stochastic control</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/4195/ZR-13-34.pdf</file>
  </doc>
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