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 (Campus-only Access)

Subjects

Dissertations, Academic -- Sciences; Sciences -- Dissertations, Academic

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