An immuno-epidemiological model linking within-host and between-host dynamics of cholera

Cholera, an acute gastrointestinal disease caused by the bacterium Vibrio cholerae, continues to be a major threat to public health with an estimated 1.3 - 4 million cases reported annually. The majority of existing cholera models focus on the between-host dynamics independent of within-host dynamics, a factor that downplays the interdependence of the two processes on the spread of the infection. In this study, an immuno-epidemiological model for cholera is formulated to analyze the effect of within- host dynamics on the population. The model is an adaptation of the immuno-epidemiological models reviewed by M. Martcheva, N. Tuncer, C. St Mary (2015). We use time-scale methods to distinguish the dynamics of the immune response and the parasite load of an individual. A thorough bifurcation analysis reveals the existence of a saddle node and Hopf bifurcation. In contrast to other immunological models, the present approach allows for clearance of the pathogen after a finite time. The between- host system is represented by a size structured model with the pathogen load considered as the linking mechanism. We derive expressions for the reproduction number and conduct stability analysis of the equilibria. Conclusions about the interdependence of the two dynamics on disease spread are drawn from the analysis.