Rich dynamics of a bidirectionally linked immuno-epidemiological model for cholera.

Cholera is an environmentally driven disease where the human hosts both ingest the pathogen from polluted environment and shed the pathogen to the environment, generating a two-way feedback cycle. In this paper, we propose a bidirectionally linked immuno-epidemiological model to study the interaction of within- and between-host cholera dynamics. We conduct a rigorous analysis for this multiscale model, with a focus on the stability and bifurcation properties of each feasible equilibrium. We find that the parameter that represents the bidirectional connection is a key factor in shaping the rich dynamics of the system, including the occurrence of the backward bifurcation and Hopf bifurcation. Numerical results illustrate a practical application of our model and add new insight into the prevention and intervention of cholera epidemics.