Modelling the transmission dynamics and optimal control strategies for waterborne pathogen spreading with applications to cholera in Haiti

In order to depict the immunosuppressive effect induced by environmental pollution and the impact of limited resources, this paper establishes an aquatic pathogen transmission model with saturated treatment rate and immunosuppression. The threshold dynamics of the model have been analyzed based on the basic reproduction number. It is found that the existence of saturated treatment function leads to rich bifurcation phenomena in the model, including transcritical, saddle-node and Hopf bifurcations. While, the immunosuppressive effect induced by environmental pollution increases the risk of infection. Furthermore, an application is demonstrated by investigating the cholera outbreak in Haiti, and the relevant optimal control problem and control strategies are given by sensitivity analysis.