Applied Modeling and Quantitative Methods

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,

Medication used to treat human illness is one of the greatest developments in human history. In Canada, prescription drugs have been developed and made available to treat a wide variety of illnesses, from infections to heart disease and so on. Records of prescription drug fulfillment at coarse Canadian geographic scales were obtained from Health Canada in order to track the use of these drugs by the Canadian population.

The obtained prescription drug fulfillment records were in a variety of inconsistent formats, including a large selection of years for which only paper tabular records were available (hard copies). In this work, we organize, digitize, proof and synthesize the full available data set of prescription drug records, from paper to final database. Extensive quality control was performed on the data before use. This data was then analyzed for temporal and spatial changes in prescription drug use across Canada from 1990-2013.

In addition, one of major research areas in environmental epidemiological studies is the study of population health risk associated with exposure to ambient air pollution. Prescription drugs can moderate public health risk, by reducing the drug user's physiological symptoms and preventing acute health effects (e.g., strokes, heart attacks, etc.). The cleaned prescription drug data was considered in the context of a common model to examine its influence on the association between air pollution exposure and various health outcomes. Since, prescription drug data were available only at the provincial level, a Bayesian hierarchical model was employed to include the prescription drugs as a covariate at regional level, which were then combined to estimate the association at national level. Although further investigations are required, the study results suggest that the prescription drugs influenced the air pollution related public health risk.

Author Keywords: Data, Error checking, Population health, Prescriptions

As the generation of genetic data accelerates, Big Data has an increasing impact on the way bioinformatics software is used. The experiments become larger and more complex than originally envisioned by software designers. One way to deal with this problem is to use parallel computing.

Using the program Structure as a case study, we investigate ways in which to counteract the challenges created by the growing datasets. We propose an OpenMP and an OpenMP-MPI hybrid parallelization of the MCMC steps, and analyse the performance in various scenarios.

The results indicate that the parallelizations produce significant speedups over the serial version in all scenarios tested. This allows for using the available hardware more efficiently, by adapting the program to the parallel architecture. This is important because not only does it reduce the time required to perform existing analyses, but it also opens the door to new analyses, which were previously impractical.

Author Keywords: Big Data, HPC, MCMC, parallelization, speedup, Structure

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

With the exponential growth of the Internet, performance is an issue as bandwidth is often limited. A scalable solution to reduce the amount of bandwidth required is Web caching. Web caching (especially at the proxy-level) has been shown to be quite successful at addressing this issue. However as the number and needs of the clients grow, it becomes infeasible and inefficient to have just a single Web cache. To address this concern, the Web caching system can be set up in a distributed manner, allowing multiple machines to work together to meet the needs of the clients. Furthermore, it is also possible that further efficiency could be achieved by balancing the workload across all the Web caches in the system. This thesis investigates the benefits of load balancing in a distributed Web caching environment in order to improve the response times and help reduce bandwidth.

Author Keywords: adaptive load sharing, Distributed systems, Load Balancing, Simulation, Web Caching

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

This thesis focuses on the design of a modelling framework consisting of loose-coupling of a sequence of spatial and process models and procedures necessary to predict future flood events for the years 2030 and 2050 in Tabasco Mexico. Temperature and precipitation data from the Hadley Centers Coupled Model (HadCM3), for those future years were downscaled using the Statistical Downscaling Model (SDSM4.2.9). These data were then used along with a variety of digital spatial data and models (current land use, soil characteristics, surface elevation and rivers) to parameterize the Soil Water Assessment Tool (SWAT) model and predict flows. Flow data were then input into the Hydrological Engineering Centers-River Analysis System (HEC-RAS) model. This model mapped the areas that are expected to be flooded based on the predicted flow values. Results from this modelling sequence generate images of flood extents, which are then ported to an online tool (ADAPT) for display. The results of this thesis indicate that with current prediction of climate change the city of Villahermosa, Tabasco, Mexico, and the surrounding area will experience a substantial amount of flooding. Therefore there is a need for adaptation planning to begin immediately.

Author Keywords: Adaptation Planning, Climate Change, Extreme Weather Events, Flood Planning, Simulation Modelling

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

The conversion of historical analog images to time series data was performed by using deconvolution for pre-processing, followed by the use of custom built digitization algorithms. These algorithms have been developed to be user friendly with the objective of aiding in the creation of a data set from decades of mechanical observations collected from the Agincourt and Toronto geomagnetic observatories beginning in the 1840s. The created algorithms follow a structure which begins with pre-processing followed by tracing and pattern detection. Each digitized magnetogram was then visually inspected, and the algorithm performance verified to ensure accuracy, and to allow the data to later be connected to create a long-running time-series.

Author Keywords: Magnetograms

The AeolianBox is an educational and presentation tool extended in this thesis to

represent the atmospheric boundary layer (ABL) flow over a deformable surface in the

sandbox. It is a hybrid hardware cum mathematical model which helps users to visually,

interactively and spatially fathom the natural laws governing ABL airflow. The

AeolianBox uses a Kinect V1 camera and a short focal length projector to capture the

Digital Elevation Model (DEM) of the topography within the sandbox. The captured

DEM is used to generate a Computational Fluid Dynamics (CFD) model and project the

ABL flow back onto the surface topography within the sandbox.

AeolianBox is designed to be used in a classroom setting. This requires a low

time cost for the ABL flow simulation to keep the students engaged in the classroom.

Thus, the process of DEM capture and CFD modelling were investigated to lower the

time cost while maintaining key features of the ABL flow structure. A mesh-time

sensitivity analysis was also conducted to investigate the tradeoff between the number of

cells inside the mesh and time cost for both meshing process and CFD modelling. This

allows the user to make an informed decision regarding the level of detail desired in the

ABL flow structure by changing the number of cells in the mesh.

There are infinite possible surface topographies which can be created by molding

sand inside the sandbox. Therefore, in addition to keeping the time cost low while

maintaining key features of the ABL flow structure, the meshing process and CFD

modelling are required to be robust to variety of different surface topographies.

To achieve these research objectives, in this thesis, parametrization is done for meshing process and CFD modelling.

The accuracy of the CFD model for ABL flow used in the AeolianBox was

qualitatively validated with airflow profiles captured in the Trent Environmental Wind

Tunnel (TEWT) at Trent University using the Laser Doppler Anemometer (LDA). Three

simple geometries namely a hemisphere, cube and a ridge were selected since they are

well studied in academia. The CFD model was scaled to the dimensions of the grid where

the airflow was captured in TEWT. The boundary conditions were also kept the same as

the model used in the AeolianBox.

The ABL flow is simulated by using software like OpenFoam and Paraview to

build and visualize a CFD model. The AeolianBox is interactive and capable of detecting

hands using the Kinect camera which allows a user to interact and change the topography

of the sandbox in real time. The AeolianBox's software built for this thesis uses only

opensource tools and is accessible to anyone with an existing hardware model of its

predecessors.

Author Keywords: Augmented Reality, Computational Fluid Dynamics, Kinect Projector Calibration, OpenFoam, Paraview