Analysis of a “phase transition” from tumor growth to latency

A mathematical model, based on the local interaction simulation approach, is developed in order to allow simulations of the spatiotemporal evolution of neoplasies. The model consists of a set of rules, which govern the interaction of cancerous cells among themselves and in competition with other cell populations for the acquisition of essential nutrients. As a result of small variations in the basic parameters, it leads to four different outcomes: indefinite growth, metastasis, latency, and complete regression. In the present contribution a detailed analysis of the dormant phase is carried on and the critical parameters for the transition to other phases are computed. Interesting chaotic behaviors can also be observed, with different attractors in the parameters space. Interest in the latency phase has been aroused by therapeutical strategies aiming to reduce a growing tumor to dormancy. The effect of such strategies may be simulated with our approach.