  The immune system protects the body against health-threatening entities,
known as antigens, through very complex interactions involving the antigens and
the system's own entities. One remarkable feature resulting from such
interactions is the immune system's ability to improve its capability to fight
antigens commonly found in the individual's environment. This adaptation
process is called the evolution of specificity. In this paper, we introduce a
new mathematical model for the evolution of specificity in humoral immunity,
based on Jerne's functional, or idiotypic, network. The evolution of
specificity is modeled as the dynamic updating of connection weights in a graph
whose nodes are related to the network's idiotypes. At the core of this
weight-updating mechanism are the increase in specificity caused by clonal
selection and the decrease in specificity due to the insertion of uncorrelated
idiotypes by the bone marrow. As we demonstrate through numerous computer
experiments, for appropriate choices of parameters the new model correctly
reproduces, in qualitative terms, several immune functions.
