Effects of correlated noise in a tumor cell growth model in the presence of immune response

The effects of correlated noises in a tumor cell growth model in the presence of immune response under the simultaneous action of correlated multiplicative and additive white noise and a weak periodic signal are investigated. The analytical expression of the signal-to-noise ratio (SNR) for the model is obtained by using the theory of SNR in the adiabatic limit. Based on the numerical computations, it is found that (i) a maximum appears in the curve of SNR as a function of cross-correlation intensity λ in the region of λ> 0, i.e. this is a resonant peak, and (ii) for the case of λ>0, the curve of SNR as a function of additive noise intensity α exhibits a minimum first and then a maximum, that is to say, it exhibits suppression first and resonance later. But for the case of λ≤0, the resonant peak of the SNR-α curve disappears.