Stochastic and deterministic multipatch epidemic models

Hasler, Jordan J

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https://hdl.handle.net/2142/90745 Copy

Description

Title

Stochastic and deterministic multipatch epidemic models

Author(s)

Hasler, Jordan J

Issue Date

2016-04-15

Director of Research (if dissertation) or Advisor (if thesis)

DeVille, Lee

Doctoral Committee Chair(s)

Rapti, Zoi

Committee Member(s)

• Zharnitsky, Vadim
• Kirkpatrick, Kay

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2016-05

Type of Resource

text

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http://hdl.handle.net/2142/90745

Copyright and License Information

Copyright 2016 Jordan Hasler

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