An age-structured model for cholera control with vaccination

We formulate an age-structured cholera model with four partial differential equations describing the transmission dynamics of human hosts and one ordinary differential equation representing the bacterial evolution in the environment. We conduct rigorous analysis on the trivial (disease-free) and non-trivial (endemic) equilibria of the system, and establish their existence, uniqueness, and stability where possible. Meanwhile, we perform an optimal control study for the age-structured model and seek effective vaccination strategies that best balance the outcome of vaccination in reducing cholera infection and the associated costs. Our modeling, analysis and simulation emphasize the complex interplay among the environmental pathogen, the human hosts with explicit age structure, and the age-dependent vaccination as a disease control measure.