Mathematical Modelling of Natural Phenomena

Research Article

Mathematical and Computational Models in Tumor Immunology

F. Pappalardoa1, A. Palladinia1, M. Pennisi, F. Castiglionea3 and S. Motta c1

a1 Università degli Studi di Catania, Catania, Italy

a2 Cancer Research Section, Department of Experimental Pathology, University of Bologna, Bologna, Italy

a3 Institute for Computing Applications "M. Picone", National Research Council of Italy, Viale Manzoni 30, 00185 Rome, Italy


The immune system is able to protect the host from tumor onset, and immune deficiencies are accompanied by an increased risk of cancer. Immunology is one of the fields in biology where the role of computational and mathematical modeling and analysis were recognized the earliest, beginning from 60s of the last century. We introduce the two most common methods in simulating the competition among the immune system, cancers and tumor immunology strategies: differential equations and rule-based models. Several specific implementations are presented, describing in details how they work and how they advance or contribute the field of tumor immunology.

(Online publication June 06 2012)

Key Words:

  • cancers;
  • tumor immunology;
  • agent based models;
  • mathematical modeling;
  • vaccines

Mathematics Subject Classification:

  • 81T80;
  • 92B05;
  • 46N60;
  • 62P10;
  • 92C60


c1 Corresponding author. E-mail: