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Programme

The Final Oral Examination
for the Degree of
Master of Science

(Department of Mathematics and Statistics)

Seyedeh Shaghayegh AhooeiNejad
Shahid Beheshti University, B.Sc. in Statistics (2022)

Breeding Patterns of Ancient Murrelet: A Multievent Model Approach

April 15, 2025
10:30 am
Zoom: https://uvic.zoom.us/j/83320849914

Supervisory Committee:
Dr. Laura Cowen, Department of Mathematics and Statistics, UVic (Supervisor)
Dr. Simon Bonner, Department of Mathematics and Statistics, UVic (Member)

Chair of Oral Examination:
Dr. Peter Dukes, Department of Mathematics and Statistics, UVic

See announcement and abstract (PDF).

See announcement and abstract (PDF)

Notice of the Final Oral Examination for the Degree of Doctor of Philosophy of

MANTING WANG

MSc (Donghua University, 2020)
BSc (Huaibei Normal University, 2017)

“Deterministic and Stochastic Modelling of Infectious Diseases in the Early Stages”

Department of Mathematics and Statistics
Friday, April 11, 2025
10:00 A.M.
Clearihue Building
Room B019

Supervisory Committee:
Dr. Junling Ma, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Pauline van den Driessche, Department of Mathematics and Statistics, UVic (Co-Supervisor)
Dr. Dean Karlen, Department of Physics and Astronomy, UVic (Outside Member)

External Examiner:
Dr. Michael Li, Department of Mathematical and Statistical Sciences, University of Alberta

Chair of Oral Examination:
Dr. Mihai Sima, Department of Electrical and Computer Engineering, UVic

Abstract
During the early stages of an epidemic, case counts typically grow exponentially, influenced by disease transmissibility, contact patterns, and implemented control measures. Understanding this exponential growth and disentangling the effects of various interventions are critical for public health decision-making. This dissertation investigates the dynamics of the early stages of an epidemic under control measures, addressing two key topics: evaluating the effectiveness of contact tracing and estimating the exponential growth rate of cases.

Contact tracing is a key public health measure to reduce disease transmission. However, due to limited public health capacity, it is mostly effective during the early stage when the case counts are low. In Chapter 2, I develop a novel modelling framework to track contacts in a randomly mixed population. This approach borrows the idea of edge dynamics from network models to track contacts included in a compartmental SIR model for an epidemic spreading. Using COVID-19 as a case study, I evaluate the effectiveness of contact tracing during the early stage when multiple control measures were implemented in Chapter 3. I conduct a simulation study to determine the necessary dataset for parameter estimation. I find that new case counts, cases identified through contact tracing (or voluntary testing), and symptomatic onset counts are necessary for parameter identification. Finally, I apply our models to the early stages of the COVID-19 pandemic in Ontario, Canada.

Chapters 4 and 5 focus on reliably estimating the exponential growth rate during the early stages of an outbreak, a key measure of the speed of disease spread. To establish a suitable likelihood function for accurate growth rate estimation, I derive the probability generating function for new cases using a linear stochastic SEIR model and obtain formulas for its mean and variance in Chapter 4. Numerical simulations show that the binomial or negative binomial distribution closely approximates the distribution of new cases. To determine the most appropriate method for estimating the growth rate, I compare the performance of the negative binomial regression model and the hidden Markov model (HMM) in Chapter 5. My results show that the 95% credible intervals produced by the HMM have a higher probability of covering the true growth rate.

The Final Oral Examination for the Degree of

Master of Science
(Department of Mathematics and Statistics)

Farbod Esmaeili
Shahid Beheshti University, B.Sc. in Statistics (2022)

“A Comparative Review of Stock Market Forecasting Models with a Simulation Study on GARCH Dynamics”

December 12, 2024
3:00 pm
Zoom: https://uvic.zoom.us/j/83893006823

Supervisory Committee:
Dr. Farouk Nathoo, Department of Mathematics and Statistics, UVic (Supervisor) Dr. Min Tsao, Department of Mathematics and Statistics, UVic (Member)

Chair of Oral Examination:
Dr. Peter Dukes, Department of Mathematics and Statistics, UVic

The Final Oral Examination for the Degree of Master of Science

(Department of Mathematics and Statistics)

Naresh Neupane
MA, University of Victoria (2020)
BSc, Southeastern Louisiana University (2016)

“Optimal Designs for Quadratic, Cubic, Quartic and Quintic Polynomial Models in Balls”

December 13, 2024
1:30 pm
DTB A203

Supervisory Committee:
Dr. Julie Zhou, Department of Mathematics and Statistics, UVic (Supervisor)
Dr. Min Tsao, Department of Mathematics and Statistics, UVic (Member)

Chair of Oral Examination: Dr. Junling Ma, Department of Mathematics and Statistics, UVic

Examining Committee

Supervisory Committee
Dr. Rod Edwards, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Anthony Quas, Department of Mathematics and Statistics, UVic (Member)

External Examiner
Dr. Bastien Fernandez, Laboratoire de Probabilités Statistique and Modélisation, French National Centre for Scientific Research

Chair of Oral Examination
Dr. Eva Kwoll, Department of Geography, UVic

Meeting link: https://uvic.zoom.us/j/87448763654

Abstract
Electronic circuitry based on chaotic Glass networks, a type of piecewise smooth dynamical system, has recently been proposed as a potential design for true random number generators. Glass networks are good designs due to their potential for chaotic behaviour and because their analytic tractability allows us here to propose a method for approximating their entropy, a measure of irregularity in dynamical systems. We discuss some of the historical developments that led to the interest in the model that we consider within the context of random number generation. Additionally, we discuss a method for converting a Glass network’s governing piecewise-smooth differential equations into discrete-time dynamical systems, and then into symbolic dynamical systems. We also detail how the symbolic entropy of the given Glass network is bounded above by the entropy of the symbolic dynamical system formed from its transition graph, a type of directed graph that represents the possible transitions in phase space between regions not containing discontinuities. We then extend previous results by detailing our new method of refining the transition graph to be a more accurate depiction of the true system’s dynamics, making use of more specific information about trapping regions in phase space. Refinements come in the form of splitting nodes and duplicating/partitioning edges on the transition graph and removing those that are never realized by the continuous dynamics. We show that refinements can be done to arbitrary levels and in the limit as the level of refinement goes to infinity, the entropy of the refined transition graphs converges to the true entropy of the system. Along with this, since it is not possible to calculate the limiting value, approximation is necessary. Doing this by hand is tedious and difficult, so as a result, we also detail here an algorithm we devised that automates the refinement process, allowing for approximation (from above) of symbolic entropy. Various examples are considered throughout and we also discuss how numerical simulation can be used to non-rigorously estimate symbolic entropy, as an independent (approximate) verification of our results. Finally, we detail some unfinished and future work which could extend our results further, along with alternative methods to achieve similar and potentially even stronger results. With our results and algorithm, using upper bounds on a Glass network’s symbolic representation’s entropy is now a viable method for assessing the irregularity of its dynamics.