Abstract
The problem of understanding how biological species and infectious diseases can persist and spread in heterogeneous networks has brought a wide attention, recently highlighted due to the COVID-19 pandemic. This dissertation investigates the connection between the structures of heterogeneous networks and population persistence/disease invasion. To do so, we propose a new index for network heterogeneity by employing the Laplacian matrix of population dispersal and its corresponding group inverse. The network growth rate and reproduction number can be evaluated using the network average and the network heterogeneity index as the first and second order approximation, respectively. We also illustrate the impact of arrangement of ecological sources/sinks and disease hotspots/non-hotspots, which highlights the significance of the network structures on population persistence and disease invasion in heterogeneous environments. Mathematically, population and disease control strategies can be modeled via altering certain ecological and epidemiological parameters in the biological processes. To quantitatively measure the scale of the change in need, new indices and methods are introduced and developed to generalize the existing threshold parameters. Properties and implications of these are provided to demonstrate the applicability to infectious disease controls such as anthrax, cholera and Zika virus.
Notes
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Graduation Date
2022
Semester
Fall
Advisor
Shuai, Zhisheng
Degree
Doctor of Philosophy (Ph.D.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematics
Format
application/pdf
Identifier
CFE0009424; DP0027147
URL
https://purls.library.ucf.edu/go/DP0027147
Language
English
Release Date
December 2022
Length of Campus-only Access
None
Access Status
Doctoral Dissertation (Open Access)
STARS Citation
Yazdanbakhshghahyazi, Poroshat, "Population Persistence and Disease Invasion in Heterogenous Networks" (2022). Electronic Theses and Dissertations, 2020-2023. 1453.
https://stars.library.ucf.edu/etd2020/1453