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Human Health Modelling: Delay Differential Equations Inverse Problems and a Model of the Minamata Pollution Epidemic

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Title: Human Health Modelling: Delay Differential Equations Inverse Problems and a Model of the Minamata Pollution Epidemic
Author: Yodzis, Michael
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: Kunze, HerbBauch, ChrisAnand, Madhur
Abstract: This thesis presents a theoretical framework to solve inverse problems for delayed ordinary differential equations (delay ODEs), and draws on results from real analysis, fixed point theory, and delay ODEs existence-uniqueness theory for its justification. To implement the method, we develop techniques to manage the piecewise integration of time-delayed arguments, and use non-convex optimization to recover unknown delay values. The method is tested on simulated and noised datasets to estimate unknown parameters for models applied to human health. The second part of this thesis develops a human-environmental system model for the effects of water pollution on the health and livelihood of a fishing community in the developing world. The model is motivated by data from the methylmercury-poisoning incident in Minamata, Japan (c.1949-1968). We examine the conditions that cause the outbreak of a pollution-induced epidemic, and study the role of social feedbacks and misperception effects that allow the epidemic to persist.
URI: http://hdl.handle.net/10214/8368
Date: 2014-07
Rights: Attribution-NonCommercial-NoDerivs 2.5 Canada
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Attribution-NonCommercial-NoDerivs 2.5 Canada Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs 2.5 Canada