  In spite of their many facets, the phenomena of autoimmunity and
immunodeficiency seem to be related to each other through the subtle links
connecting retroviral mutation and action to immune response and adaptation. In
a previous work, we introduced a network model of how a set of interrelated
genotypes (called a quasispecies, in the stationary state) and a set of
interrelated idiotypes (an idiotypic network) interact. That model, which does
not cover the case of a retroviral quasispecies, was instrumental for the study
of quasispecies survival when confronting the immune system and led to the
conclusion that, unlike what happens when a quasispecies is left to evolve by
itself, letting genotypes mutate too infrequently leads to the destruction of
the quasispecies. Here we extend that genotype-idiotype interaction model by
the addition of a further parameter ($\nu$) to account for the action of
retroviruses (i.e., the destruction of idiotypes by genotypes). We give
simulation results within a suitable parameter niche, highlighting the issues
of quasispecies survival and of the onset of autoimmunity through the
appearance of the so-called pathogenic idiotypes. Our main findings refer to
how $\nu$ and $\lambda$, a parameter describing the rate at which idiotypes get
stimulated, relate to each other. While for $\nu>\lambda$ the quasispecies
survives at the expense of weakening the immune system significantly or even
destroying it, for $\nu<\lambda$ the fittest genotypes of the quasispecies
become mimicked inside the immune system as pathogenic idiotypes. The latter is
in agreement with the current understanding of the HIV quasispecies.
