Spatio-temporal dynamics of an age-space structured cholera model with bacterial hyperinfectivity and imperfect vaccination

Cholera is a waterborne disease caused by the bacterium Vibrio cholerae. Laboratory findings suggested that passage through the human host transiently increased the infection potential of the bacteria by creating a hyperinfectious bacterial state, which may contribute to the epidemic spread of cholera. In this paper, we are concerned with the global asymptotic behavior of an infection age-space structured cholera model with multiple transmission pathways, hyperinfectious and hypoinfectious vibrios, imperfect vaccination, and distinct dispersal rates for humans in a general continuous bounded domain under Neumann boundary condition. The mathematical challenges stem from the following facts: (i) the model is partially degenerate, and the solution is not compact; (ii) the imperfect vaccination is incorporated into an infection age-space structured model with multiple transmission pathways. By analyzing the corresponding characteristic equations and constructing suitable Lyapunov functionals, the basic reproduction number is determined as a threshold to predict whether the infection will persist. Numerical simulations support our theoretical results and suggest that compared with increasing the vaccination rate of susceptible humans, enhancing vaccine efficacy is more conducive to reducing the basic reproduction number and controlling cholera spread.