An Immuno-epidemiological Model Linking Between-host and Within-host Dynamics of Cholera

TL;DR

This paper develops a comprehensive immuno-epidemiological model for cholera that links within-host immune dynamics with between-host transmission, providing insights into disease control and pathogen elimination.

Contribution

It introduces a novel multi-scale model connecting within-host immune responses with population-level transmission, including bifurcation analysis and pathogen elimination conditions.

Findings

Pathogen can be eliminated after finite time in the model.

Basic reproduction number derived and stability analyzed.

Endemic equilibrium is globally stable without immunity loss.

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.