Effects That Cause the Instability of the Positive Equilibrium for Simple Pathogen Dynamics Models

Abstract

It is well known that a time delay can cause the instability of the equilibrium. In the case of pathogen dynamics models, the absorption effect (when pathogens invade target cells, they are absorbed into cells and disappear from blood) also can cause the instability. Besides the two effects above, introducing an immune response variable into a pathogen dynamics model can cause the instability. This paper shows, for the models lacking one or more of the three effects, the positive equilibrium is always stable. Moreover, it shows that, for the model incorporating all the three effects, the positive equilibrium can be unstable.