Dynamical analysis and control strategies in modeling cholera

We conduct rigorous stability analysis for the well-known cholera model proposed by Codeço [7]. Using theory of monotone dynamical systems, we prove that the endemic equilibrium, when it exists, of the model is globally asymptotically stable, implying the persistence of the disease in the absence of interventions. We then modify Codeço’s model by incorporating various control strategies, and study the subsequent dynamics. We find that with strong control measures, the basic reproduction number will be reduced below 1 so that the disease-free equilibrium is globally asymptotically stable. With weak controls, instead, a unique and globally stable endemic equilibrium would still occur, though at a lower infection level. The analytical predictions are confirmed by numerical simulation results.