This study focuses on the world dynamics of a cholera model that includes delayed bacterial shedding and water disinfection. From the method of the next generation matrix, a basic reproduction number is found that sets a threshold of disease persistence. It is shown that the disease disappears if $R_0<1$, which means that the disease-free equilibrium is globally asymptotically stable. The system is not destabilized by the delay, which leads to periodic oscillations. The numerical simulations validate the theoretical analysis, which illustrates the importance of delay and disinfection in cholera prevention and control.
Author Keywords: Basic reproduction number, Cholera, Delay differential equations, Disinfection, Lyapunov function, Stability analysis