title: Global stability and uniform persistence of the reaction-convection-diffusion cholera epidemic model.
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.
authors.affiliation: Department of Mathematics, University of Rochester, Rochester, NY 14627, United States. email: kyamazak@ur.rochester.edu.
authors.forename: Kazuo
authors.initials: K
authors.lastname: Yamazaki
authors.forename: Xueying
authors.initials: X
authors.lastname: Wang
mesh_terms: D050936:Basic Reproduction Number; D002771:Cholera / Q000453:epidemiology*; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008954:Models, Biological; D014871:Water Microbiology