title: A generalized cholera model and epidemic-endemic analysis.
abstract: The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R (0)=1 for the combined human-environment epidemiological model under biologically reasonable conditions.
authors.affiliation: Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA. j3wang@odu.edu
authors.forename: Jin
authors.initials: J
authors.lastname: Wang
authors.forename: Shu
authors.initials: S
authors.lastname: Liao
mesh_terms: D002771:Cholera / Q000453:epidemiology*; D003198:Computer Simulation; D019353:Endemic Diseases / Q000706:statistics & numerical data*; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D008954:Models, Biological; D012111:Residence Characteristics / Q000706:statistics & numerical data