Local Immunodeficiency: Minimal Networks and Stability

Leonid Bunimovich, Longmei Shu

Published 2018-08-11Version 1

Some basic aspects of the recently discovered phenomenon of local immunodeficiency \cite{pnas} generated by antigenic cooperation in cross-immunoreactivity networks are investigated. We prove that stable under perturbations local immunodeficiency already occurs in very small networks and under general conditions on their parameters. A major necessary feature of such networks is non-homogeneity of their topology. It is also shown that one can construct larger cross-immunoreactivity networks with stable local immunodeficiency by using small networks with stable local immunodeficiency as their building blocks. Our results imply that stable local immunodeficiency occurs in networks with quite general topology. In particular the scale-free property of a cross-imunoreactivity network, assumed in \cite{pnas}, is not required.