Lyapunov functions; heterogeneous sir model; global asymptotic stability; generalized incidence; nonlinear incidence; disease dynamics; mathematical epidemiology
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.
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Master of Science (M.S.)
College of Sciences
Mathematical Science; Industrial Mathematics
Length of Campus-only Access
Masters Thesis (Open Access)
Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic
Wilda, Joseph, "Analysis and Simulation for Homogeneous and Heterogeneous SIR Models" (2015). Electronic Theses and Dissertations, 2004-2019. 1260.