Modeling vaccine protocols.

Mathematical models are quantitative representation of phenomena built up in the framework of a theory using the language of mathematics. Living organisms are natural complex systems and modelling may play a crucial role since models can also be built with approximate and imperfect knowledge of the phenomenon and model parameters (initial data, entities, relations between entities) can be adjusted to fit modeling results to experimental measurements. These models can then be used to understand general behavior of the phenomenon in different situations; perform model experiments or simulations to understand the role of single constituents and relations; plan new experiments; test theoretical assumptions and suggest theory modifications. Modelling can therefore stimulate scientific creativity and produce better theoretical descriptions of the reality. We describe here our efforts in the creation of models of the immune system and of the competition between immune defenses and tumor cells. We developed an agent-based model of the effects of a vaccine designed to prevent mammary carcinoma incidence in transgenic mice. This model faithfully recapitulates not only the outcome of vaccination experiments, but also the dynamics of immune responses elicited by the vaccine. We then used a genetic algorithm to drive the model and predict optimized vaccination schedules which are currently being tested in vivo. We discuss here also the implications of biologic diversity on model development and the perpspectives to develop natural-scale models of the immune system.