Hopf Bifurcation in a Delayed Cholera Model Incorporating Bacterial Growth and Phage–Vibrio Interactions

Cholera is a severe diarrheal illness triggered by Vibrio cholerae, and it continues to pose a lasting global challenge to public health. This paper formulates a delayed cholera model by including bacterial growth and phage–vibrio interactions. The basic reproduction number Formula: see text and the phage invasion reproduction number Formula: see text are obtained. Through mathematical analysis, the existence conditions for Hopf bifurcation and stability switch at the phage-present endemic equilibrium are derived when Formula: see text. By employing the center manifold theory, properties of Hopf bifurcation are further discussed. Through the construction of proper Lyapunov functionals and the use of LaSalle’s invariance principle, the global asymptotic stability of the disease-free equilibrium is established when Formula: see text, whereas infected hosts and V. cholerae become persistent when Formula: see text. Numerical simulations are conducted to show the main theoretical results. In addition, taking the cholera epidemic in Lusaka in 2017–2018 as an example, parameter estimation and data fitting are performed. Finally, the sensitivity analysis suggests that the interaction between bacteriophages and V. cholerae helps reduce the number of infected hosts to a more manageable level.