Threshold Dynamics of a Chronological Age and Infection Age Structured Cholera Model with Neumann Boundary Condition

ge and spatial heterogeneities play a significant role in the prediction of transmission patterns of the cholera prevalence. In this paper, we propose a diffusive cholera epidemic model with chronological age and infection age structures. First, we adopt some embedding tricks and transform the model into a non-densely Cauchy problem. Then we establish the existence, uniqueness and dissipativity of the model by the integral semigroup and the Volterra integral equation theory. Finally, we show that the global dynamics of each feasible equilibrium determined by the basic reproduction number ℛ_0 . If ℛ_0<1 , the disease-free equilibrium is globally asymptotically stable; if ℛ_0>1 , the endemic equilibrium E^* is globally attractive as long as the shedding rate of an infected individual is a function of chronological age or infection age.