Deterministic and stochastic modelling of infectious diseases in the early stages

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dc.contributor.authorWang, Manting
dc.contributor.supervisorMa, Junling
dc.contributor.supervisorVan den Driessche, Pauline
dc.date.accessioned2025-04-29T20:14:24Z
dc.date.available2025-04-29T20:14:24Z
dc.date.issued2025
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelDoctor of Philosophy PhD
dc.description.abstractDuring 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.
dc.description.scholarlevelGraduate
dc.identifier.bibliographicCitationBednarski S, Cowen LL, Ma J, Philippsen T, van den Driessche P, Wang M. A contact tracing SIR model for randomly mixed populations. Journal of Biological Dynamics. 2022 Dec 31;16(1):859-79.
dc.identifier.bibliographicCitationWang M, Ma J, van den Driessche P, Cowen LL. Estimating the Effect of Contact Tracing During the Early Stage of an Epidemic. Infectious Disease Modelling. 2025 Feb 13.
dc.identifier.urihttps://hdl.handle.net/1828/22042
dc.languageEnglisheng
dc.language.isoen
dc.rightsAvailable to the World Wide Web
dc.subjectCompartmental disease model
dc.subjectControl reproduction number
dc.subjectPair dynamics
dc.subjectTracing coverage
dc.subjectTracing capacity
dc.subjectStochastic SEIR model
dc.subjectProbability generating function
dc.subjectNegative binomial distribution
dc.subjectNew cases
dc.subjectUnstable manifold approximationprevalence
dc.subjectExponential growth rate
dc.subjectHidden Markov model
dc.titleDeterministic and stochastic modelling of infectious diseases in the early stages
dc.typeThesis

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