Modeling and analysis of a diffusive cholera model with seasonally forced intrinsic incubation period and bacterial hyperinfectivity

Abstract

In order to explore the impact of a seasonally forced intrinsic incubation period, bacterial hyperinfectivity, and environmental heterogeneity on the cholera spatiotemporal transmission dynamics, we construct a diffusive cholera model with a seasonal forced intrinsic incubation period and bacterial hyperinfectivity with non-flux boundary condition. The seasonally forced intrinsic incubation period is the period of time that pathogens spend in completing their development in the host, which extends the concept of the fixed latency period by introducing the seasonal impacts of the environment. We derive the basic reproduction number ℜ0 and investigate the threshold dynamics for exploring whether the model retains the core properties that are highly desirable in epidemic models, that is, the spread of cholera can be characterized by ℜ0. In a homogeneous case, we also establish the global attractivity of the unique constant endemic equilibrium by the technique of Lyapunov functional.