title: Influence of diffusion on the stability of equilibria in a reaction-diffusion system modeling cholera dynamic.
abstract: 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.
authors.affiliation: Department of Mathematics and Applications 'R. Caccioppoli', University of Naples Federico II, Complesso Universitario Monte S. Angelo, Via Cinzia, 80126 , Naples, Italy. fcapone@unina.it.
authors.forename: Florinda
authors.initials: F
authors.lastname: Capone
authors.affiliation: Department of Mathematics and Applications 'R. Caccioppoli', University of Naples Federico II, Complesso Universitario Monte S. Angelo, Via Cinzia, 80126 , Naples, Italy. valentina.decataldis@unina.it.
authors.forename: Valentina
authors.initials: V
authors.lastname: De Cataldis
authors.affiliation: Department of Mathematics and Applications 'R. Caccioppoli', University of Naples Federico II, Complesso Universitario Monte S. Angelo, Via Cinzia, 80126 , Naples, Italy. roberta.deluca@unina.it.
authors.forename: Roberta
authors.initials: R
authors.lastname: De Luca
mesh_terms: D002771:Cholera / Q000453:epidemiology* / Q000635:transmission; D003198:Computer Simulation; D004197:Disease Reservoirs / Q000382:microbiology / Q000706:statistics & numerical data; D058872:Epidemics / Q000706:statistics & numerical data; D006205:Haiti / Q000453:epidemiology; D006801:Humans; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D014734:Vibrio cholerae / Q000302:isolation & purification; D014871:Water Microbiology
keywords: Cholera; Epidemic models; Lyapunov direct method; Reaction–diffusion systems; Stability