  This paper analyzes the role of neutral viruses in the phenomenon of local
immunodeficiency. We show that, even in the absence of altruistic viruses,
neutral viruses can support the existence of persistent viruses, and thus local
immunodeficiency. However, in all such cases neutral viruses can maintain only
bounded (relatively small) concentration of persistent viruses. Moreover, in
all such cases the state of local immunodeficiency could only be marginally
stable, while it is known that altruistic viruses can maintain stable local
immunodeficiency. We also present an absolutely minimal cross-immunoreactivity
network where a stable and robust state of local immunodeficiency can be
maintained. It is now a challenge to synthetic biology to build such small
networks with stable local immunodeficiency. Another important challenge for
biology is to understand which types of viruses can play a role of persistent,
altrustic and neutral ones, and whether a role which a given virus plays
depends on the structure (topology) of a given cross-immunoreactivity network.
