The primary CD8 T-cell response, due to a first encounter
between a pathogen and the CD8-type adaptive immune system, consists of
two phases: an expansion phase, with a fast increase of T-cell count,
followed by a contraction phase. This contraction phase is followed by
the generation of memory cells, specic of the antigen and allowing a
faster and stronger response when encountering the antigen for the
second time.
We propose a model of the primary CD8 T cell response, based on
age-structured transport equations, in which nonlinearities account for
molecular regulation of cell dynamics. We will discuss the roles and
relevance of feedback controls that could regulate the response,
investigate the local asymptotic stability of the system and prove the
global asymptotic stability of the trivial equilibrium when considering
a biologically realistic primary infection. Then, we will use this model
to estimate parameter values (T cell death rates, proliferation rates,
etc.) by confronting a simpler version of the model, based on a system
of nonlinear ordinary differential equations, to experimentally
generated data. The presentation will end up with a brief discussion on
the problem at the molecular scale, and how one can deal with regulatory
networks invoved in such a response.
