Effect of Time Delay in the Stability Analysis of Cholera Epidemic-Endemic Disease Model

Abstract

Cholera as a disease is a kind of acute diarrhea caused by bacteria Vibrio cholerae. A nonlinear delayed mathematical model with environmental factor for the spread of infectious disease cholera is proposed and analyzed. A mathematical model for cholera was improved by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. It is assumed that all susceptible are affected by carrier population density. The model is analyzed by stability theory of differential equations and computer simulation. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. Both the disease-free (DFE) and endemic equilibria are found and their stability investigated using the Routh-Hurwitz stability criterion method. Next Generation Matrix (NGM) method was used to get the basic reproductive number