Antigenic cooperation in viral populations: Maximal load on viruses and self-sufficiency of persistent viruses

The paper continues the study of the phenomenon of local immunodeficiency in viral cross-immunoreactivity networks, with a focus on the roles and interactions between central and persistent viral variants. As usual, only the state of stable (i.e. observable) local immunodeficiency is analyzed. First, we show that a single central viral variant has an upper limit for the number of persistent viral variants that it can support. Our findings reveal that in viral cross-immunoreactivity networks, central viruses act essentially autonomously from each other. Namely, connections between central viruses change neither their qualitative roles nor the quantitative values of the strengths of their connections in the cross-immunoreactivity networks. In other words, each central virus does exactly the same actions, and has the same strengths with or without specific structural features such as central viruses. This indicates that local immunodeficiency can arise purely from the network structure. However, having more central viruses allows to keep the sizes of populations of persistent viruses at higher levels. Likewise, the strength of the immune response against any central virus remains at the same constant level regardless of how many persistent viruses this central virus supports (i.e. shields from the immune response of the host's immune system). It is also shown that viruses strongly compete with each other in order to become persistent in the state of stable local immunodeficiency. We also present an (quite unexpected) example of a cross-immunoreactivity network with stable local immunodeficiency that only consists of persistent viral variants, which shows that persistent viruses may demonstrate a kind of self-consistency.