Thesis Defence: Perturbation theory of linear systems with applications to structured SIR models

Md Tareque Hossain, supervised by Dr. Eric Foxall, will defend their thesis titled “Perturbation theory of linear systems with applications to structured SIR models” in partial fulfillment of the requirements for the degree of Master of Science in Mathematics.

An abstract for Md Tareque Hossain’s thesis is included below.

Defences are open to all members of the campus community as well as the general public. Registration is not required for in person defences.

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ABSTRACT

We explore the impact of parameter changes on infection spread within structured populations. By studying perturbations of linear models in both discrete and continuous time and interpreting the resulting formulas in the context of an associated Markov chain, new insights are gained. Specifically, we explain how the rate of change of key quantities, that we represent with the so-called canonical flow, is determined by expected hitting times of corresponding states in the Markov chain, from different initial distributions. We give intuitive, direct proofs of known results, and obtain novel formulae in the case of a general primitive or irreducible Metzler matrix. We apply our results to two models from the literature: the fast pathogen movement limit of a structured model of Cholera spread and the slow-fast decomposition of critical structured SIR models near the disease-free set. We explain how the latter context can be used to model the effects of control measures with uncontrolled response variables.