Narrow Results

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be very costly. By resolving the fast time scales in a short time simulation, a model for the effect of the small time scale variation on large time scales can be determined, making solution possible on a long time interval. This process of computational modeling can be completely automated. Two examples are presented, including a simple model problem oscillating at a time scale of 10^–9 computed over the time interval [0,100], and a lattice consisting of large and small point masses.

The aim of this paper is to discuss biological and computational models of tumor-immune system interactions. To this end we provid first a short introduction to the field of general immunology, then a more in-depth exposition of cancer immunology. Finally we discuss a first approach to vaccine that prevent tumor onset from a biological point of view and we describe how to reproduce this phenomenon from a computational model.