Stochastic and deterministic multipatch epidemic models

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 γ, 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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Hasler, Jordan J

Contributors dc:contributor

• DeVille, Lee
• Rapti, Zoi
• Zharnitsky, Vadim
• Kirkpatrick, Kay

• epidemics
• dynamical systems
• stochastic processes
• SIR

Statement dc:rights

• Copyright 2016 Jordan Hasler

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/90745