Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and.pdf

a r X i v : 0 7 1 0 .1 3 1 7 v 3 [ p h y s i c s .b i o - p h ] 1 5 M a y 2 0 0 8 EPJ manuscript No. (will be inserted by the editor) Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment Alessandro Fiasconaro 123 a , Anna Ochab–Marcinek 24 , Bernardo Spagnolo 3 , and Ewa Gudowska–Nowak 12 1 Mark Kac Complex Systems Research Center, Jagellonian University, Reymonta 4, 30-059 Krako?w, Poland. 2 Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krako?w, Poland. 3 Dipartimento di Fisica e Tecnologie Relative and CNISM, Group of Interdisciplinary Physics, Universita? di Palermo, Viale delle Scienze, I-90128 Palermo, Italy. 4 Institut fu?r Physik, Universita?t Augsburg, Universita?tsstra?e 1, 86135 Augsburg, Germany. May 15, 2008 Abstract. In the paper we investigate a mathematical model describing the growth of tumor in the presence of im- mune response of a host organism. The dynamics of tumor and immune cells is based on the generic Michaelis-Menten kinetics depicting interaction and competition between the tumor and the immune system. The appropriate phenomeno- logical equation modeling cell-mediated immune surveillance against cancer is of the predator-prey form and exhibits bistability within a given choice of the immune response-related parameters. Under the influence of weak external fluctuations, the model may be analyzed in terms of a stochastic differential equation bearing the form of an over- damped Langevin-like dynamics in the external quasi-potential represented by a double well. We analyze properties of the system within the range of parameters for which the potential wells are of the same depth and when the additional perturbation, modeling a periodic treatment, is insufficient to overcome the barrier height and to cause cancer extinc- tion. In this case the presence of a small amount of noise can positively enhance the treatment, driving the system to a s