Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model

Kazuo Yamazaki; Xueying Wang

doi:10.3934/mbe.2017033

Mathematical Biosciences and Engineering, 2017, 14(2): 559-579. doi: 10.3934/mbe.2017033.

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Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model

Kazuo Yamazaki, Xueying Wang

1. Department of Mathematics, University of Rochester, Rochester, NY 14627, USA
2. Department of Mathematics and Statistics, Washington State University, Pullman, WA 99164-3113, USA

Received: , Accepted: , Published:

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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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Keywords: Basic reproduction number; cholera dynamics; persistence; principal eigenvalues; stability

Citation: Kazuo Yamazaki, Xueying Wang. Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model. Mathematical Biosciences and Engineering, 2017, 14(2): 559-579. doi: 10.3934/mbe.2017033

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