Bacterial infections elicit immune responses including neutrophils, whose recruitment is stimulated by the bacteria’s presence but which die after eliminating those bacteria. This dual interaction between bacteria and neutrophil concentrations, more complicated than the simple predator-prey relationship that describes macrophage-bacteria interactions, creates an environment in which neutrophils may only be able to clear sufficiently small infections. This study describes this relationship using a simple nonlinear dynamical system which exhibits bistability behavior known as a backward bifurcation. Bacterial growth is assumed limited by a key nutrient. In contrast to a previous study which held neutrophil and nutrient levels constant and required saturation terms to produce bistability, our model shows that simple bilinear terms support bistability when nutrient and neutrophil densities are allowed to vary in response to bacterial density. An example application involving Borrelia burgdorferi, which feeds on manganese, illustrates why neutrophils’ rapid response is key to their ability to contain bacterial infections.
Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion