Axiomatic modeling is ensued to provide a family of models that describe bacterial growth in
the presence of phagocytes, or, more generally, prey dynamics in a large spatially
homogenous eco-system. A classification of the possible bifurcation diagrams that arise in
such models is presented. It is shown that other commonly used models that do not belong
to this class may miss important features that are associated with the limited growth curve of
the bacteria (prey) and the saturation associated with the phagocytosis (predator kill) term …