Stability and bifurcation analysis of cholera model

In this paper, we present and analyze a nonlinear mathematical model for the cholera, an infection of the small intestine caused by the bacterium Vibrio cholerae. Our model is a system of nonlinear ordinary differential equations. By using threshold condition of the model, we present conditions that guarantee occurrence transcritical bifurcation. Finally, the numerical simulation of the model using Oscill illustrates our analytical results.