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A reaction-diffusion system modeling cholera epidemic in a non-homogeneously mixed population is introduced. The interaction between population and toxigenic Vibrio cholerae concentration in contaminated water has been taken into account. The existence of biologically meaningful equilibria is investigated together with their linear and nonlinear stability. Using the data collected during the Haiti cholera epidemic, a numerical simulation is performed.

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A nonlinear energy stability analysis of the onset of convection for fluids with viscosity depending exponentially on temperature is performed. It is shown that the condition assuring linear stability assures nonlinear asymptotic stability, too