A stochastic model for the activation of T-cells is analysed. T-cells are
part of the immune system and recognize foreign antigens against a background
of the body's own molecules. The model under consideration is a slight
generalization of a model introduced by Van den Berg, Rand and Burroughs in
2001, and is capable of explaining how this recognition works on the basis of
rare stochastic events. With the help of a refined large deviation theorem and
numerical evaluation it is shown that, for a wide range of parameters, T-cells
can distinguish reliably between foreign antigens and self-antigens.Comment: 16 pages, 6 figures; minor revision, new simulations; J Math Biol.,
in pres
