An Immuno-epidemiological Model Linking Between-host and Within-host Dynamics of Cholera (2105.12675v1)

Abstract: Cholera, a severe gastrointestinal infection caused by the bacterium Vibrio cholerae, remains a major threat to public health with a yearly estimated global burden of 2.9 million cases. Although the majority of existing models for the disease focus on its population dynamics, it's important to link the multiple scales of the disease to gain better perspectives on its spread and control. In this study, we formulate an immuno-epidemiological model for cholera linking the between-host and within-host dynamics of the disease. The within-host model utilizes time-scale methods to differentiate the pathogen dynamics from the dynamics of the immune response. Bifurcation analysis of the within-host system reveals the necessary conditions for the existence of both the Hopf and saddle-node bifurcations. Contrary to other within-host models, the current approach allows for the elimination of the pathogen after a finite time. The epidemic model takes into account the direct human-to-human transmission route of the infection as well as the transmission via the environment. It is represented by a dynamical system structured on the immune status, which is a function derived from the within-host immune response. The basic reproduction number is derived and the stability of equilibrium points analysed. Analysis of the endemic equilibrium reveals additional constraints that lead to its stability. Without loss of immunity, the endemic equilibrium, if it exists, is globally asymptotically stable.