  In previous work, we studied host response to a pathogen which uses a cycle
of immunologically distinct stages to establish and maintain infection. We
showed that for generic parameter values, the system has a unique biologically
meaningful stable fixed point. That paper used a simplified model of T-cell
activation, making proliferation depend linearly on antigen-T-cell encounters.
Here we generalize the way in which T-cell proliferation depends on the sizes
of the antigenic populations. In particular, we allow this response to become
saturated at high levels of antigen. As a result, we show that this family of
generalized models shares the same steady-state behavior properties with the
simpler model contemplated in our previous work.
