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Mathematical Modeling of Infectious Diseases with Latency: Homogeneous Mixing and Contact Network

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Date Issued:
2016
Abstract/Description:
In mathematical epidemiology, the standard compartmental models assume homogeneous mixingin the host population, in contrast to the disease spread process over a real host contact network. One approach to incorporating heterogeneous mixing is to consider the population to be a networkof individuals whose contacts follow a given probability distribution. In this thesis we investigate in analogy both homogeneous mixing and contact network models for infectious diseases that admit latency periods, such as dengue fever, Ebola, and HIV. We consider the mathematics of thecompartmental model as well as the network model, including the dynamics of their equations from the beginning of disease outbreak until the disease dies out. After considering the mathematical models we perform software simulations of the disease models. We consider epidemic simulationsof the network model for three different values of R0 and compare the peak infection numbers and times as well as disease outbreak sizes and durations. We examine averages of these numbers for one thousand simulation runs for three values of R0. Finally we summarize results and consider avenues for further investigation.
Title: Mathematical Modeling of Infectious Diseases with Latency: Homogeneous Mixing and Contact Network.
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Name(s): Carlson, Keith, Author
Shuai, Zhisheng, Committee Chair
Mohapatra, Ram, Committee CoChair
Guha, Ratan, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2016
Publisher: University of Central Florida
Language(s): English
Abstract/Description: In mathematical epidemiology, the standard compartmental models assume homogeneous mixingin the host population, in contrast to the disease spread process over a real host contact network. One approach to incorporating heterogeneous mixing is to consider the population to be a networkof individuals whose contacts follow a given probability distribution. In this thesis we investigate in analogy both homogeneous mixing and contact network models for infectious diseases that admit latency periods, such as dengue fever, Ebola, and HIV. We consider the mathematics of thecompartmental model as well as the network model, including the dynamics of their equations from the beginning of disease outbreak until the disease dies out. After considering the mathematical models we perform software simulations of the disease models. We consider epidemic simulationsof the network model for three different values of R0 and compare the peak infection numbers and times as well as disease outbreak sizes and durations. We examine averages of these numbers for one thousand simulation runs for three values of R0. Finally we summarize results and consider avenues for further investigation.
Identifier: CFE0006276 (IID), ucf:51054 (fedora)
Note(s): 2016-08-01
M.S.
Sciences, Psychology
Masters
This record was generated from author submitted information.
Subject(s): infectious disease
network
edge-based compartmental model
latency
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0006276
Restrictions on Access: public 2016-08-15
Host Institution: UCF

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