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 〉 s t 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.