Open Collections

Hossain, Md Tareque

University of British Columbia

We explore the impact of parameter changes on infection spread within structured populations. We study perturbations of linear models in both discrete and continuous time. By 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 cor- responding states in the Markov chain, from different initial distributions. We give intuitive direct proofs of known results and obtain novel formulas 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.

Text

2023-12-14

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86957

Mathematics

University of British Columbia

UBCO

http://creativecommons.org/licenses/by-nc-nd/4.0/