  Mathematical modeling and analysis can provide insight on the dynamics of
ecosystems which maintain biodiversity in the face of competitive and
prey-predator interactions. Of primary interests are the underlying structure
and features which stabilize diverse ecological networks. Recently Korytowski
and Smith [17] proved that a perfectly nested infection network, along with
appropriate life history trade-offs, leads to coexistence and persistence of
bacteria-phage communities in a chemostat model. In this article, we generalize
their model in order to apply it to the within-host dynamics virus and immune
response, in particular HIV and CTL (Cytotoxic T Lymphocyte) cells. Our model
can produce a diverse hierarchy of viral and immune populations, built through
sequential viral escape from dominant immune responses and rise in subdominant
immune responses, consistent with observed patterns of HIV/CTL evolution. We
find a Lyapunov function for the system which leads to rigorous
characterization of persistent viral and immune variants, and informs upon
equilibria stability and global dynamics. Results are interpreted in the
context of within-host HIV/CTL evolution and numerical simulations are
provided.
