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","Master of Science (M.S.)","College of Sciences","Mathematics","Mathematical Science; Industrial Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Analysis and Simulation for Homogeneous and Heterogeneous SIR Models"]}]}],"canonical_facts":{"dc:contributor":["Shuai, Zhisheng"],"dc:creator":["Wilda, Joseph"],"dc:description":["If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu
","Master of Science (M.S.)","College of Sciences","Mathematics","Mathematical Science; Industrial Mathematics"],"dc:description.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."],"dc:format":["application/pdf"],"dc:identifier":["CFE0005906"],"dc:identifier.uri":["https://stars.library.ucf.edu/etd/1260"],"dc:language":["English"],"dc:subject":["Lyapunov functions; heterogeneous sir model; global asymptotic stability; generalized incidence; nonlinear incidence; disease dynamics; mathematical epidemiology","Mathematics","Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic"],"dc:title":["Analysis and Simulation for Homogeneous and Heterogeneous SIR Models"],"dc:type":["Masters Thesis (Open Access)"]},"updated_at":"2026-07-24T05:09:59Z"}