<div class="csl-bib-body">
<div class="csl-entry">Widder, A. (2016). <i>Aggregation and optimisation in epidemiological models of heterogeneous populations</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2016.37465</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2016.37465
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/6574
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dc.description
Abweichender Titel nach Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
This thesis is concerned with the analysis of models of heterogeneous populations in infectious disease epidemiology. Special considerations are made with respect to variables arising from the aggregation of heterogeneous variables. We analyse the asymptotic behaviour, steady states, and stability of simple heterogeneous SI-, SIS-, and SIR-models with parametric heterogeneity, which are described by an infinite dimensional system of ODEs. As for homogeneous models, we are able to define a basic reproduction number which can be used as an indicator for the existence of endemic steady states and stability of disease free steady states. In some cases a finite dimensional ODE system for the aggregated variables can be formulated, which simplifies both analysis and practical calculations. For SIS-models we also consider the influence of heterogeneity on early warning signs for critical transitions. We develop a stochastic model to incorporate fluctuation effects and the random import of the disease into the population. We analyse the influence of heterogeneity on warning signs for critical transitions. This theory shows that one may be able to anticipate whether a bifurcation point is close before it happens. Using numerical simulations, we show that known scaling laws for early warning signs no longer hold true for heterogeneous models. We identify various different ways in which heterogeneity can influence these scaling laws. This is of importance if one wants to interpret potential warning signs for disease outbreaks. One obstacle to applying heterogeneous models in practice is that in order for the equations to be well defined it is necessary to have knowledge of the initial conditions for the distributed heterogeneous variables. This information is in many cases not available. However, the variables of interest are often not the heterogeneous variables, but their aggregated counterparts. We therefore develop set-membership estimation techniques for these aggregated variables under the assumption that the initial conditions for the heterogeneous variables are only partially known. By numerically solving certain optimisation problems we are able to calculate these estimations. Furthermore, we consider optimal control problems for heterogeneous systems. For models with parametric heterogeneity, we show by example how aggregation techniques can in certain cases be used to reduce the infinite dimensional problem to a finite dimensional one, for which the well developed standard optimal control theory can be applied. We also develop a version of Pontryagin's maximum principle for heterogeneous systems that include aggregated variables. We do this not in the framework of parametric heterogeneity, but more generally for size structured PDEs.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
mathematische Epidemologie
de
dc.subject
heterogene epidemologische Modelle
de
dc.subject
Set-membership Schätzung
de
dc.subject
größenstrukturierte Systeme
de
dc.subject
optimale Kontrolle von heterogenen Systemen
de
dc.subject
mathematical epidemology
en
dc.subject
heterogeneous epidemological models
en
dc.subject
set-membership estimation
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dc.subject
size-structured systems
en
dc.subject
optimal control of hetergeneous systems
en
dc.title
Aggregation and optimisation in epidemiological models of heterogeneous populations
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dc.title.alternative
Aggregation und Optimierung in epidemiologischen Modellen heterogener Populationen
de
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2016.37465
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Andreas Widder
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dc.publisher.place
Wien
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E105 - Institut für Stochastik und Wirtschaftsmathematik
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dc.type.qualificationlevel
Doctoral
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dc.identifier.libraryid
AC13247220
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dc.description.numberOfPages
164
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-3480
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dc.thesistype
Dissertation
de
dc.thesistype
Dissertation
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.fulltext
with Fulltext
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item.cerifentitytype
Publications
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_db06
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item.languageiso639-1
en
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item.openaccessfulltext
Open Access
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item.openairetype
doctoral thesis
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item.grantfulltext
open
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crisitem.author.dept
E105 - Institut für Stochastik und Wirtschaftsmathematik