  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.
