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Title:Mathematical models of daphnia epidemics
Author(s):Rivera Quinones, Vanessa
Director of Research:Rapti, Zoi
Doctoral Committee Chair(s):Laugesen, Richard
Doctoral Committee Member(s):DeVille, Lee; Caceres, Carla
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):disease ecology
rapid evolution
Daphnia
epidemic models
recovery
host-parasite
resource competition
Quantitative Genetics
Adaptive Dynamics
mathematical models
Partial differential equations
Stochastic models
Gillespie Algorithm
Abstract:Disease ecology studies the interactions among hosts, pathogens, and the environment and how these shape the spread of disease. These interactions can be quite complex and lead to fascinating dynamics. Our system of study, Daphnia has a lot of interesting and complex features that can be analyzed with precision both biologically and mathematically. By using mathematical models we can study the underlying biological mechanisms that drive and/or inhibit the spread of disease. This dissertation explores, through a range of models, the many aspects that play a role in Daphnia epidemics. We begin with simple models and build models with higher complexity by adding more realistic biological assumptions. From ordinary and partial differential equation models to stochastic models, through the chapters of this thesis, we zoom-in to the different aspects of Daphnia epidemics and and zoom-out to the bigger story that connects them. We give precise conditions under which short-term evolution of hosts can lead to the early termination of an epidemic. Moreover, overturning an assumption about hosts’ ability to recover, we showcase the role of recovery from an infection in reducing disease prevalence and the number of secondary infections. Through this thesis we have gained more insight into the biology of our system, and more importantly we open the door to new and exciting questions. As new biological insights are discovered, we can use mathematical models to continue to unravel the many aspects of Daphnia epidemics.
Issue Date:2019-07-01
Type:Text
URI:http://hdl.handle.net/2142/105612
Rights Information:Copyright 2019 Vanessa Rivera Quinones
Date Available in IDEALS:2019-11-26
Date Deposited:2019-08


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