Infectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Network

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dc.contributor.authorBoneng, Joanna Felicia
dc.date.accessioned2016-09-26T19:23:32Z
dc.date.available2016-09-26T19:23:32Z
dc.date.issued2016-09-26
dc.date.submitted2016-09-22
dc.description.abstractIn this thesis, we study deterministic compartmental epidemic models. The conventional mass-mixing assumption is replaced with infectious disease contraction occurring within a heterogeneous network. Modeling infectious diseases with a heterogeneous contact network divides disease status compartments into further sub-compartments by degree class and thus allows for the finite set of contacts of an individual to play a role in disease transmission. These epidemiological network models are introduced as switched systems, which are systems that combine continuous dynamics with discrete logic. Many models are investi- gated, including SIS, SIR, SIRS, SEIR type models, and multi-city models. We analyze the stability of these switched network models. Particularly, we consider the transmission rate as a piecewise constant that changes value according to a switching signal. We establish threshold criteria for the eradication of a disease or stability of an endemic equilibrium using Lyapunov function techniques. Simulations are also conducted to support our claims and conclude conjectures. We test constant control and pulse control schemes, including vaccination, treatment, and screening processes for the application of these infectious disease models. Necessary critical control values are determined for the eradication of the disease.en
dc.identifier.urihttp://hdl.handle.net/10012/10914
dc.language.isoenen
dc.pendingfalse
dc.publisherUniversity of Waterlooen
dc.subjectinfectious disease modelingen
dc.subjectnetworken
dc.subjectepidemiologyen
dc.subjectswitched systemsen
dc.subjecthybrid systemsen
dc.subjectscale-free networken
dc.titleInfectious Disease Modeling with Interpersonal Contact Patterns as a Heterogeneous Networken
dc.typeMaster Thesisen
uws-etd.degreeMaster of Mathematicsen
uws-etd.degree.departmentApplied Mathematicsen
uws-etd.degree.disciplineApplied Mathematicsen
uws-etd.degree.grantorUniversity of Waterlooen
uws.contributor.advisorLiu, Xinzhi
uws.contributor.affiliation1Faculty of Mathematicsen
uws.peerReviewStatusUnrevieweden
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.scholarLevelGraduateen
uws.typeOfResourceTexten

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