Dynamical behavior of cholera epidemic model with non-linear incidence rate

Cholera is an infection of the small intestine caused by the bacterium Vibrio cholera. In this work, we consider a mathematical model SIRB which represents the dynamics of cholera. To understand the dynamics of the model, the disease free and endemic stability are discussed. The disease free equilibrium is stable locally as well as globally when the basic reproduction less than 1, otherwise an unstable equilibrium exist. If the basic reproduction number exceeds than unity, then the endemic equilibrium is stable locally as well as globally with some sufficient conditions. The numerical solution of the model illustrates the analytical results. © 2014.