Problems in Theoretical Immunology

Abstract

Immunology¹ is not a new field of research: the first vaccinations against smallpox were done by the end of the seventeenth century by Jenner. But the practice of vaccination, although much more intricate than described in elementary textbooks, remained largely empirical. The important successes of experimental methods derived from immunology in molecular biology never had much counterpart from the theoretical point of view. Only a few models of infection, based on population dynamics, have been proposed. Until quite recently most immunologists considered that clinical conditions could be explained by the presence or absence of some specific macromolecules or cell types. Such simple approaches have in fact been sufficient to handle efficiently a number of clinical and experimental problems. It is only quite recently that the self /non-self recognition problem led N. Jerne² to formulate his network hypothesis, and that people realized that the consequences of the hypothesis could only be checked through some effort in theoretical modeling^{3, 4}. Before presenting our contribution let us review the important characteristics of the immune response that are indispensable to the understanding of our model.