Journal article
Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model
Mathematical biosciences and engineering : MBE, Vol.14(2), pp.559-579
04/01/2017
Handle:
https://hdl.handle.net/2376/104339
PMID: 27879114
Abstract
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is beneath one, we show that the disease-free-equilibrium is globally attractive. On the other hand, when the basic reproduction number exceeds one, if the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, we prove the uniform persistence result and that there exists at least one positive steady state.
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Details
- Title
- Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model
- Creators
- Kazuo Yamazaki - Department of Mathematics, University of Rochester, Rochester, NY 14627, United States. email: kyamazak@ur.rochester.eduXueying Wang
- Publication Details
- Mathematical biosciences and engineering : MBE, Vol.14(2), pp.559-579
- Academic Unit
- Mathematics and Statistics, Department of
- Publisher
- United States
- Identifiers
- 99900547089901842
- Language
- English
- Resource Type
- Journal article