  We analyze a within-host model of virus infection with antibody and CD8+
cytotoxic T lymphocyte (CTL) responses proposed by Schwartz et al. (2013). The
goal of this work is to gain an overview of the stability of the
biologically-relevant equilibria as a function of the model's immune response
parameters. We show that the equilibria undergo at most two forward
transcritical bifurcations. The model is also explored numerically and results
are applied to equine infectious anemia virus infection. In order to arrive at
stability of the biologically-relevant endemic equilibrium characterized by
coexistence of antibody and CTL responses, the parameters promoting CTL
responses need to be boosted over parameters promoting antibody production.
This result may seem counter-intuitive (in that a weaker antibody response is
better) but can be understood in terms of a balance between CTL and antibody
responses that is needed to permit existence of CTLs. In conclusion, an
intervention such as a vaccine that is intended to control a persistent viral
infection with both immune responses should moderate the antibody response to
allow for stimulation of the CTL response.
