Stability and control analysis of a Cholera model structured by infection-age with hyperinfectivity and population movement

This study examines an age-structured Cholera epidemic model that integrates both hyperinfectious and non-hyperinfectious strains of Vibrio cholera, while accounting for the immigration impact of the infected population. The model comprises a first-order partial differential equation in conjunction with a system of three ordinary differential equations. A rigorous analytical study, based on semi-group theory, confirms the existence of a unique, positive and bounded solution. We further establish the existence and global asymptotic stability of a unique endemic equilibrium. The study depends on core concepts such as uniform persistence and asymptotic smoothness, which assist the establishment of a suitable Lyapunov functional. A vaccination strategy is employed as a control variable, leading to the formulation and settlement of an optimal control problem utilizing the generalized Pontryagin’s Maximum Principle. We perform numerical simulations by using Wendland’s Compactly Supported Radial Basis Functions together with the finite difference method of characteristics. The findings validate the theoretical results in guiding the system toward equilibrium and confirm the effectiveness of the proposed control mechanism.