Stability and optimal control of a cholera transmission model with waning vaccine-induced immunity and phage-vibrio interactions

Cholera is still a significant worldwide health concern that continues to affect many regions around the world, posing a persistent threat to human health with its severity unabated. In this paper, a cholera transmission model with waning vaccine-induced immunity and phage-vibrio interactions is investigated. The two important thresholds for distinguishing whether cholera is epidemic or not are obtained, and fundamental properties of the system are studied. The global asymptotic stability of the system is analyzed in detail by constructing suitable Lyapunov functions. To seek the suitable strategies for preventing and controlling cholera infection, we introduced four time-dependent controls into the model to assess the effectiveness of each strategy by applying Pontryagin's maximum principle. In addition, using the reported cholera case numbers in Yemen, we perform parameter estimation and data fitting, further, a sensitivity analysis of thresholds is conducted.