Threshold-type result for a nonlocal diffusive cholera model with seasonally forced intrinsic incubation period

In the current study, we formulated and analyzed a nonlocal diffusive cholera model incorporating the spatial heterogeneous structure, and seasonally forced intrinsic incubation period for demonstrating the infection dynamics between humans and vibrios in the environment. Here the intrinsic incubation period is the developmental duration for the vibrios within human populations, which is assumed to be $ \omega $-periodic in time. We establish the well-poseness of the model and study the threshold-type result in terms of the basic reproduction number by introducing the next generation operator. Specifically, we confirm the result that in a homogeneous case, the unique positive equilibrium is globally attractive, achieved by Lyapunov functional.