Transitions induced by time delays and cross-correlated sine-Wiener noises in a tumor-immune system interplay

A model of tumor-immune system interplay with time delays and cross-correlated sine-Wiener noises is investigated by numerical simulations for the stationary probability distribution (SPD) and stationary mean value 〈x〉_st of tumor cell population. Results show that (i) the structure of the SPD transfers from bimodal to unimodal as the reaction time (τ_α) of the cell population to environmental constraints increases; (ii) conversely, as the time (τ_β) of immune system to develop specific immune competence and the correlation time (τ) of noises increase, the structure of the SPD transfers from unimodal to bimodal; (iii) as the cross-correlated intensity (λ^′) between noises increases, the transitions induced by τ are suppressed.