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 Title: Stochastic and deterministic multipatch epidemic models Author(s): Hasler, Jordan J Director of Research: DeVille, Lee Doctoral Committee Chair(s): Rapti, Zoi Doctoral Committee Member(s): Zharnitsky, Vadim; Kirkpatrick, Kay Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): epidemics dynamical systems stochastic processes SIR Abstract: This dissertation covers the modeling of epidemics in populations that contain multiple groups that also includes interaction between subgroups. The main techniques employed are thresholds for both the deterministic and the stochastic system through an approximating multi-type branching process. We formulate a continuous time Markov Chain that corresponds to each deterministic system studied. The main idea will be to study the spectral radius of the next generation matrix with regards to crossing of a critical threshold (corresponding to stability) with regards to the parameter $\gamma$, which measures the amount of interaction between each of the groups. We include numerical approximations of the ordinary differential equation (ODE). We also derive how the continuous time is an actual approximation through the theory of Darling and Norris. We further give examples of comparing all three: spectral data, the actual ODE numerical results, and the stochastic approximation. We further study how modifying the parameters modifies the properties of the model. Multiple examples for each model are given in both the paper and the end material. We also discuss how the graph structure modifies the ability of an epidemic to spread. Issue Date: 2016-04-15 Type: Thesis URI: http://hdl.handle.net/2142/90745 Rights Information: Copyright 2016 Jordan Hasler Date Available in IDEALS: 2016-07-07 Date Deposited: 2016-05
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