Stability analysis of simple models for immune cells interacting with normal pathogens and immune system retroviruses

A mathematical analysis is presented for several simple dynamical systems that might be considered as crude descriptions for the situation when an immune system retrovirus, immune cells, and normal autonomously replicating pathogens interact. By stability analysis of the steady-state solutions, the destabilizing effect of the immune system retrovirus is described. The qualitative behavior of the solutions depending on the system parameters is analyzed in terms of trajectories moving in a phase space in which the axes are defined by the population numbers of the interacting biological entities.