2026-09-23T23:08:44Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/115721 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Rapti, Zoi DeVille, Lee Bronski, Jared Zharnitsky, Vadim 2022-05 application/pdf en text Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-05-01 The student, Shinhae Park, accepted the attached license on 2022-04-19 at 08:07. The student, Shinhae Park, submitted this Dissertation for approval on 2022-04-19 at 08:11. This Dissertation was approved for publication on 2022-04-20 at 11:01. DSpace SAF Submission Ingestion Package generated from Vireo submission #17782 on 2022-11-11 at 12:47:20 Dynamics of multiple populations interactions Park, Shinhae 2022-04-20 asymptotic stability mathematical models bistable dynamics epidemic models Covid-19 identifiability analysis input-output relations profile likelihood The main focus of this thesis is to study the dynamical systems of interacting species and populations. In the first part, we consider the generalized Lotka-Volterra equations that describe multi-species interactions, including amensalism, commensalism, mutualism, competition, and predator-prey. In particular, we revisit the results presented in [30] where we investigated the asymptotic stability of the generalized Lotka-Volterra equations with respect to the underlying network topologies, such as trees and complete graphs. It was of interest to study the coexistence (no local extinction of species) equilibrium being locally stable. We find that the techniques in proofs and stability results for the tree networks are applicable to a community described by a modified Lotka Volterra model of predator-prey interaction. We then consider specific cases where the models are modified Lotka-Volterra competition equations, exhibiting bistable dynamics which are ubiquitous in ecology. In particular, we consider a competitive model from [48] which accounts for crowding effects – high population density increases the mortality rate. It was concluded from [48] that crowding promotes the coexistence of competing species. We confirm this analytically by studying the (local and global) stability of the coexistence equilibrium and the partial extinction equilibrium. In the second part, we concentrate on infectious disease dynamics. We introduce an epidemiological model with a minimal number of parameters and study the initial stages of the COVID-19 epidemic in Belgium. Among the reported COVID-19 data, we use only hospitalization data to estimate the model parameters and evaluate the basic reproductive number R0. As the states of the model are partially observable, we perform sensitivity and uncertainty analyses in various ways in order to assess the confidence in parameter estimates. Prior to the estimation procedure, we first analyze the structural identifiability of the parameters in the model to ensure that unique solutions for the parameters. We also conduct global sensitivity analysis to investigate the influencing parameters to the model observables. After the estimation, we examine the practical identifiability of the model parameters numerically. While not all model parameters are practically identifiable, it is found that R0 is structurally and practically identifiable. Thesis eng https://hdl.handle.net/2142/115721 Copyright 2022 Shinhae Park Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics