Graduate Theses & Dissertations


Stability Properties of Disease Models under Economic Expectations
Comprehending the dynamics of infectious diseases is very important in formulating public health policies to tackling their prevalence. Mathematical epidemiology (ME) has played a very vital role in achieving the above. Nevertheless, classical mathematical epidemiological models do not explicitly model the behavioural responses of individuals in the presence of prevalence of these diseases. Economic epidemiology (EE) as a field has stepped in to fill this gap by integrating economic and mathematical concepts within one framework. This thesis investigated two issues in this area. The methods employed are the standard linear analysis of stability of dynamical systems and numerical simulation. Below are the investigations and the findings of this thesis: Firstly, an investigation into the stability properties of the equilibria of EE models is carried out. We investigated the stability properties of modified EE systems studied by Aadland et al. [6] by introducing a parametric quadratic utility function into the model, thus making it possible to model the maximum number of contacts made by rational individuals to be determined by a parameter. This parameter in particular influences the level of utility of rational individuals. We have shown that if rational individuals have a range of possible contacts to choose from, with the maximum of the number of contacts allowable for these individuals being dependent on a parameter, the variation in this parameter tends to affect the stability properties of the system. We also showed that under the assumption of permanent recovery for disease coupled with individuals observing or not observing their immunity, death and birth rates can affect the stability of the system. These parameters also have effect on the dynamics of the EE SIS system. Secondly, an EE model of syphilis infectivity among &ldquo men who have sex with men &rdquo (MSM) in detention centres is developed in an attempt at looking at the effect of behavioural responses on the disease dynamics among MSM. This was done by explicitly incorporating the interplay of the biology of the disease and the behaviour of the inmates. We investigated the stability properties of the system under rational expectations where we showed that: (1) Behavioural responses to the prevalence of the disease affect the stability of the system. Therefore, public health policies have the tendency of putting the system on indeterminate paths if rational MSM have complete knowledge of the laws governing the motion of the disease states as well as a complete understanding on how others behave in the system when faced with risk-benefit trade-offs. (2) The prevalence of the disease in the long run is influenced by incentives that drive the utility of the MSM inmates. (3) The interplay between the dynamics of the biology of the disease and the behavioural responses of rational MSM tends to put the system at equilibrium quickly as compared to its counterpart (that is when the system is solely dependent on the biology of the disease) when subjected to small perturbation. Author Keywords: economic and mathematical epidemiology models, explosive path, indeterminate-path stability, numerical solution, health gap, saddle-path stability, syphilis,
ABSTRACT The Propensity Toward Extremist Mind-Set as Predicted by Personality, Motivation, and Self-Construal Nick Fauset Multivariate regression analyses were used to determine the effects of Personality (Neuroticism, Extraversion, Openness, Agreeableness, and Conscientiousness), Motivation (External, Amotivation, Intrinsic, and Identified), and Self-Construal (Independent and Interdependent) on three domains of Extremist Mind-Set (Proviolence, Vile World, and Divine Power). Participants consisted of first year undergraduate students (209 females, 76 males) enrolled in Introductory Psychology (N=279) and/or Introductory Economics (N=7), whom participated for course credit. The Motivation measure was problematic for students to complete and this variable was dropped from the model due to missing data. Decreases in Neuroticism, Openness, Agreeableeness, and Interdependent were significantly correlated with increases in Proviolence. Decreases in Agreeableness were correlated with increases in Vile World. Decreases in Openness, and increases in Agreeableness and Interdependent were significantly correlated with increases in Divine Power. These observations provide an interesting perspective on the types of Canadian undergraduate students who are more likely to score highly on measures of Extremism. Keywords: Militant Extremist Mental Mind-Set, Extremism, Personality, Five Factor Model, Motivation, Intrinsic, Extrinsic, Self-Construal, Independent, Interdependent Author Keywords: Extremism, Militant Extremist Mental Mind-Set, Motivation, Personality, Self-Construal
An Emprirical Investigation into the Relationship Between Education and Health
Health literature has long noted a positive correlation between health and levels of education. Two competing theories have been advanced to explain this phenomenon: (1) education "causes" health by allowing individuals to process complex information and act on it; and, (2) education and health are merely correlated through some third underlying characteristic. Determining which of these two theories is correct is of importance to public policy. But that task is empirically difficult because, from the standard, static perspective, the theories are observationally equivalent. We exploit a way in which the two theories have different implications regarding the sort of behaviour we should observe over time. We use smoking as a measure of health behaviour and find that smoking rates between "high" and "low" educated individuals expand when information is hard to process, and then contract as it becomes more easily processable. This approach is then repeated using physical activity as a measure of health-related behaviour to address limitations of the smoking model. Our novel approach to estimating the differences in the behavioural responses to changes in the processability of health-related information, across education groups, provides strong evidence in support of the view that education and health are causally linked. Author Keywords: applied statistics, education, health economics, public health, public policy, smoking
An Application of the Sinc-Collocation Method in Oceanography
In this thesis, we explore the application of the Sinc-Collocation method to an oceanography model. The model of interest describes a wind-driven current with depth-dependent eddy viscosity and is formulated in two different systems; a complex-velocity system and a real-value coupled system. In general, the Sinc-based methods excel over other traditional numerical methods due to their exponentially decaying errors, rapid convergence and handling problems in the presence of singularities at end-points. In addition, the Sinc-Collocation approach that we utilize exploits first derivative interpolation, whose integration is less sensitive to numerical errors. We present several model problems to demonstrate the accuracy, and stability of the method. We compare the approximate solutions determined by the Sinc-Collocation technique with exact solutions and also with those obtained by the Sinc-Galerkin approach in earlier studies. Our findings indicate that the method we utilized outperforms those used in past studies. Author Keywords: Boundary Value Problems, Eddy Viscosity, Oceanography, Sinc Numerical Methods, Wind-Driven Currents
Modelling Submerged Coastal Environments
Built upon remote sensing and GIS littoral zone characterization methodologies of the past decade, a series of loosely coupled models aimed to test, compare and synthesize multi-beam SONAR (MBES), Airborne LiDAR Bathymetry (ALB), and satellite based optical data sets in the Gulf of St. Lawrence, Canada, eco-region. Bathymetry and relative intensity metrics for the MBES and ALB data sets were run through a quantitative and qualitative comparison, which included outputs from the Benthic Terrain Modeller (BTM) tool. Substrate classification based on relative intensities of respective data sets and textural indices generated using grey level co-occurrence matrices (GLCM) were investigated. A spatial modelling framework built in ArcGISTM for the derivation of bathymetric data sets from optical satellite imagery was also tested for proof of concept and validation. Where possible, efficiencies and semi-automation for repeatable testing was achieved using ArcGISTM ModelBuilder. The findings from this study could assist future decision makers in the field of coastal management and hydrographic studies. Keywords: Seafloor terrain characterization, Benthic Terrain Modeller (BTM), Multi-beam SONAR, Airborne LiDAR Bathymetry, Satellite Derived Bathymetry, ArcGISTM ModelBuilder, Textural analysis, Substrate classification Author Keywords:
Smote and Performance Measures for Machine Learning Applied to Real-Time Bidding
In the context of Real-Time Bidding (RTB) the machine learning problems of imbalanced classes and model selection are investigated. Synthetic Minority Oversampling Technique (SMOTE) is commonly used to combat imbalanced classes but a shortcoming is identified. Use of a distance threshold is identified as a solution and testing in a live RTB environment shows significant improvement. For model selection, the statistical measure Critical Success Index (CSI) is modified to add emphasis on recall. This new measure (CSI-R) is empirically compared with other measures such as accuracy, lift, efficiency, true skill score, Heidke's skill score and Gilbert's skill score. In all cases CSI-R is shown to provide better application to the RTB industry. Author Keywords: imbalanced classes, machine learning, online advertising, performance measures, real-time bidding, SMOTE
Effect of Listing a Stock on the S&P 500 Index on the Stock’s Volatility
This paper investigates the effect of listing a stock on the S&P 500 Index on the stock’s volatility, using various econometrics models: GARCH and EGARCH. The study mainly addresses three issues; firstly, it analyzes stock volatility in two sub-periods, secondly, it determines whether the announcement can account for the fluctuations in the price of the stock, and finally, it investigates the change in the stock’s variance. After isolating the effects of external and industry shock by using the returns on the S&P 500 Index as a proxy, the author finds evidence of structural change in the volatility of stocks after that stock is added to the index. Additionally, the existence of a dominant symmetric effect, which captures the response of volatility to news, indicate that following the onset of including the stock on the index, information flowing into the market increased. However, the rate at which old news is captured in price falls. The empirical evidence also suggests that on average a stocks variance falls and that the announcement to list a stock on the index has little effect on the stock’s price. Author Keywords: EGARCH, GARCH, S&P 500 Index, Symmetric Effect, Volatility
Modeling drought derivatives in arid regions
We propose a stochastic weather model based on temperature, precipitation, humidity and wind speed for Qatar, as a representative arid region, in order to obtain simulated values for a drought index. As a drought index, the Reconnaissance Drought Index (RDI) is commonly accepted in agriculture and is used to measure drought severity. It can be used to price weather derivatives to help farmers reduce nancial losses from drought. RDI, which is the ratio of precipitation to evapotranspiration, is calculated by considering crop growth stages. The use of dierent crop coecient value depending on the growth stage to calculate evapotranspiration can provide improved values for RDI. Additionally, six calculation methods for evapotranspiration using weather data are investigated to obtain accurate values for RDI. Author Keywords: Evapotranspiration, Markov chains, Mean reversion processes, Reconnaissance Drought Index, Stochastic dierential equations, Stochastic weather models
Application of One-factor Models for Prices of Crops and Option Pricing Process
This thesis is intended to support dependent-on-crops farmers to hedge the price risks of their crops. Firstly, we applied one-factor model, which incorporated a deterministic function and a stochastic process, to predict the future prices of crops (soybean). A discrete form was employed for one-month-ahead prediction. For general prediction, de-trending and de-cyclicality were used to remove the deterministic function. Three candidate stochastic differential equations (SDEs) were chosen to simulate the stochastic process; they are mean-reverting Ornstein-Uhlenbeck (OU) process, OU process with zero mean, and Brownian motion with a drift. Least squares methods and maximum likelihood were used to estimate the parameters. Results indicated that one-factor model worked well for soybean prices. Meanwhile, we provided a two-factor model as an alternative model and it also performed well in this case. In the second main part, a zero-cost option package was introduced and we theoretically analyzed the process of hedging. In the last part, option premiums obtained based on one-factor model could be compared to those obtained from Black-Scholes model, thus we could see the differences and similarities which suggested that the deterministic function especially the cyclicality played an essential role for the soybean price, thus the one-factor model in this case was more suitable than Black-Scholes model for the underlying asset. Author Keywords: Brownian motion, Least Squares Method, Maximum Likelihood Method, One-factor Model, Option Pricing, Ornstein-Uhlenbeck Process
Long-term Financial Sustainability of China's Urban Basic Pension System
Population aging has become a worldwide concern since the nineteenth century. The decrease in birth rate and the increase in life expectancy will make China’s population age rapidly. If the growth rate of the number of workers is less than that of the number of retirees, in the long run, there will be fewer workers per retiree. This will apply great pressure to China’s public pension system in the next several decades. This is a global problem known as the “pension crisis”. In this thesis, a long-term vision for China’s urban pension system is presented. Based on the mathematical models and the projections for demographic variables, economic variables and pension scheme variables, we test how the changes in key variables affect the balances of the pension fund in the next 27 years. This thesis applies methods of deterministic and stochastic modeling as well as sensitivity analysis to the problem. Using sensitivity analysis, we find that the pension fund balance is highly sensitive to the changes in retirement age compared with other key variables. Monte Carlo simulations are also used to find the possible distributions of the pension fund balance by the end of the projection period. Finally, according to my analysis, several changes in retirement age are recommended in order to maintain the sustainability of China’s urban basic pension scheme. Author Keywords: China, demographic changes, Monte Carlo simulation, pension fund, sensitivity tests, sustainability
Disability-Mitigating Effects of Education on Post-Injury Employment Dynamics
Using data drawn from the Workplace Safety and Insurance Board’s (WSIB) Survey of Workers with Permanent Impairments, this thesis explores if and how the human capital associated with education mitigates the realized work-disabling effects of permanent physical injury. Using Cater’s (2000) model of post-injury adaptive behaviour and employment dynamics as the structural, theoretical, and interpretative framework, this thesis jointly studies, by injury type, the effects of education on both the post-injury probability of transitioning from non-employment into employment and the post-injury probability of remaining in employment once employed. The results generally show that, for a given injury type, other things being equal, higher levels of education are associated with higher probabilities of both obtaining and sustaining employment. Author Keywords: permanent impairment, permanent injury, post-injury employment
Agro-Ecological Zoning (AEZ) of Southern Ontario and the Projected Shifts Caused by Climate Change in the Long-term Future
This thesis proposes an agro-ecological zoning (AEZ) methodology of southern Ontario for the characterization and mapping of agro-ecological zones during the historical term (1981-2010), and their shifts into the long-term (2041-2070) projected climate period. Agro-ecological zones are homogenous areas with a unique combination of climate, soil, and landscape features that are important for crop growth. Future climate variables were derived from Earth System Models (EMSs) using a high emission climate forcing scenario from the Intergovernmental Panel on Climate Change 5th Assessment Report. The spatiotemporal shifts in agro-ecological zones with projected climate change are analyzed using the changes to the length of growing period (LGP) and crop heat units (CHU), and their manifestation in agro-climatic zones (ACZ). There are significant increases to the LGP and CHU into the long-term future. Two historical ACZs exist in the long-term future, and have decreased in area and shifted northward from their historical locations. Author Keywords: Agro-climatic Zones, Agro-ecological Zones, Agro-ecological Zoning, Climate Change, Crop Heat Units, Length of Growing Period


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Format: 2021/09/16