dc.contributor.supervisor Gumel, Abba (Mathematics), Shaun, Lui (Mathematics) en dc.contributor.author Safi, Mohammad dc.date.accessioned 2010-08-23T20:49:33Z dc.date.available 2010-08-23T20:49:33Z dc.date.issued 2010-08-23T20:49:33Z dc.identifier.uri http://hdl.handle.net/1993/4069 dc.description.abstract The quarantine of people suspected of being exposed to a disease, and the isolation of those with clinical symptoms of the disease, constitute what is probably the oldest infection control mechanism since the beginning of recorded human history. The thesis is based on using mathematical modelling and analysis to gain qualitative insight into the transmission dynamics of a disease that is controllable using quarantine and en isolation. A basic model, which takes the form of an autonomous deterministic system of non-linear differential equations with standard incidence, is formulated first of all. Rigorous analysis of the basic model shows that its disease-free equilibrium is globally-asymptotically stable whenever a certain epidemiological threshold (denoted by Rc) is less than unity. The epidemiological implication of this result is that the disease will be eliminated from the community if the use of quarantine and isolation could result in making Rc < 1. The model has a unique endemic equilibrium whenever Rc > 1. Using a Lyapunov function of Goh-Volterra type, it is shown that the unique endemic equilibrium is globally-asymptotically stable for a special case. The basic model is extended to incorporate various epidemiological and biological aspects relating to the transmission dynamics and control of a communicable disease, such as the use of time delay to model the latency period, effect of periodicity (seasonality), the use of an imperfect vaccine and the use of multiple latent and infectious stages (coupled with gamma-distributed average waiting times in these stages). One of the main mathematical findings of this thesis is that adding time delay, periodicity and multiple latent and infectious stages to the basic quarantine/isolation model does not alter the essential qualitative features of the basic model (pertaining to the persistence or elimination of the disease). On the other hand, the use of an imperfect vaccine induces the phenomenon of backward bifurcation (a dynamical feature not present in the basic model), the consequence of which is that disease elimination becomes more difficult using quarantine and isolation (since, in this case, the epidemiological requirement Rc < 1 is, although necessary, no longer sufficient for disease elimination). Numerous numerical simulations are carried out, using parameter values relevant to the 2003 SARS outbreaks in the Greater Toronto Area of Canada, to illustrate some of the theoretical findings as well as to evaluate the population-level impact of quarantine/isolation and an imperfect vaccine. In particular, threshold conditions for which the aforementioned control measures could have a positive or negative population-level impact are determined. dc.format.extent 1515565 bytes dc.format.mimetype application/pdf dc.language.iso eng en_US dc.rights info:eu-repo/semantics/openAccess dc.subject Isolation en dc.subject quarantine en dc.subject equilibria en dc.title Mathematical Analysis of The Role of Quarantine and Isolation in Epidemiology en dc.type info:eu-repo/semantics/doctoralThesis dc.type doctoral thesis en_US dc.degree.discipline Mathematics en_US dc.contributor.examiningcommittee Williams, Joseph (Mathematics) en Shamseddine, Khodr (Physics and Astronomy) Yakubu, Aziz (Howard University) dc.degree.level Doctor of Philosophy (Ph.D.) en_US dc.description.note October 2010 en
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