Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 850754, 13 pages
Research Article

A Mathematical Model of Immune-System-Melanoma Competition

Department of Mathematics & Computer Science, University of Catania, V.le A Doria 6, 95125 Catania, Italy

Received 9 March 2012; Accepted 2 April 2012

Academic Editor: Francesco Pappalardo

Copyright © 2012 Marzio Pennisi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present a mathematical model developed to reproduce the immune response entitled with the combined administration of activated OT1 cytotoxic T lymphocytes (CTLs) and Anti-CD137 monoclonal antibodies. The treatment is directed against melanoma in B16 OVA mouse models exposed to a specific immunotherapy strategy. We model two compartments: the injection point compartment where the treatment is administered and the skin compartment where melanoma tumor cells proliferate. To model the migration of OT1 CTLs and antibodies from the injection to the skin compartment, we use delay differential equations (DDEs). The outcomes of the mathematical model are in good agreement with the in vivo results. Moreover, sensitivity analysis of the mathematical model underlines the key role of OT1 CTLs and suggests that a possible reduction of the number of injected antibodies should not affect substantially the treatment efficacy.