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In the paper we investigate a mathematical model describing the growth oftumor in the presence of immune response of a host organism. The dynamics oftumor and immune cells is based on the generic Michaelis-Menten kineticsdepicting interaction and competition between the tumor and the immune system.The appropriate phenomenological equation modeling cell-mediated immunesurveillance against cancer is of the predator-prey form and exhibitsbistability within a given choice of the immune response-related parameters.Under the influence of weak external fluctuations, the model may be analyzed interms of a stochastic differential equation bearing the form of an overdampedLangevin-like dynamics in the external quasi-potential represented by a doublewell. We analyze properties of the system within the range of parameters forwhich the potential wells are of the same depth and when the additionalperturbation, modeling a periodic treatment, is insufficient to overcome thebarrier height and to cause cancer extinction. In this case the presence of asmall amount of noise can positively enhance the treatment, driving the systemto a state of tumor extinction. On the other hand, however, the same noise cangive rise to return effects up to a stochastic resonance behavior. Thisobservation provides a quantitative analysis of mechanisms responsible foroptimization of periodic tumor therapy in the presence of spontaneous externalnoise. Studying the behavior of the extinction time as a function of thetreatment frequency, we have also found the typical resonant activation effect:For a certain frequency of the treatment, there exists a minimum extinctiontime.

Monitoring noise-resonant effects in cancer growth influenced by external fluctuations and periodic treatment