Saturation effects on T-cell activation in a model of a multi-stage pathogen

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.