The complex interplay between pathogens, host factors, and the integrity and composition of the endogenous microbiome determine the course and outcome of gastrointestinal infections. The model organism Yersinia entercolitica (Ye) is one of the five top frequent causes of bacterial gastroenteritis based on the Epidemiological Bulletin of the Robert Koch Institute (RKI), 10 September 2020. A fundamental challenge in predicting the course of an infection is to understand whether co-infection with two Yersinia strains, differing only in their capacity to resist killing by the host immune system, may decrease the overall virulence by competitive exclusion or increase it by acting cooperatively. Herein, we study the primary interactions among Ye, the host immune system and the microbiota, and their influence on Yersinia population dynamics. The employed model considers commensal bacterial in two host compartments (the intestinal mucosa the and lumen), the co-existence of wt and mut Yersinia strains, and the host immune responses. We determine four possible equilibria: disease-free, wt-free, mut-free, and co-existence of wt and mut in equilibrium. We also calculate the reproduction number for each strain as a threshold parameter to determine if the population may be eradicated or persist within the host. We conclude that the infection should disappear if the reproduction numbers for each strain fall below one, and the commensal bacteria growth rate exceeds the pathogen's growth rate. These findings will help inform medical control strategies. The supplement includes the MATLAB source script, Maple workbook, and figures.
Keywords: Yersinia; co-existence equilibrium; disease-free equilibrium; gastroenteritis; reproduction number.