Keywords
Lyapunov functions; heterogeneous sir model; global asymptotic stability; generalized incidence; nonlinear incidence; disease dynamics; mathematical epidemiology
Abstract
In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented along with supporting simulations. New global stability results are established for the heterogeneous model utilizing a graph-theoretic approach and Lyapunov functions. Numerical simulations confirm nonlinear incidence gives raise to rich dynamics such as synchronization and phase-lock oscillations.
Notes
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Graduation Date
2015
Semester
Summer
Advisor
Shuai, Zhisheng
Degree
Master of Science (M.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematical Science; Industrial Mathematics
Format
application/pdf
Identifier
CFE0005906
URL
http://purl.fcla.edu/fcla/etd/CFE0005906
Language
English
Release Date
August 2018
Length of Campus-only Access
3 years
Access Status
Masters Thesis (Open Access)
Subjects
Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic
STARS Citation
Wilda, Joseph, "Analysis and Simulation for Homogeneous and Heterogeneous SIR Models" (2015). Electronic Theses and Dissertations. 1260.
https://stars.library.ucf.edu/etd/1260