Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 4: Statistical physics in biological systems II (joint session DY/BP)

DY 4.3: Vortrag

Montag, 23. März 2009, 14:45–15:00, HÜL 386

A stochastic model for tumor growth with immunization — •Thomas Bose and Steffen Trimper — Institut für Physik, Martin-Luther-Universität Halle, Germany

Much effort has been spent on revealing the mechanisms of tumor evolution. Based on these findings, we analyze tumor growth and the interaction of cancer cells with the immune system.

A deterministic component as well as a random nature is attributed to the tumor-immune interaction. More specifically, we study a stochastic model for tumor cell growth with both, a multiplicative and an additive noise term as well as cross-correlations in between. The noise includes a finite correlation time. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to internal growth processes leading to a multiplicative internal noise. Additionally the system is subjected to an external additive noise which mimics the influence of the environment of the tumor including the stochastic elements of the immune response. The stationary probability distribution is derived to analyze the influence of finite correlation time, the immunization rate and the strength of the cross-correlation on the different steady states. Furthermore, the mean-first passage time is calculated in order to find out under which conditions the tumor can suffer extinction under the effect of correlated noise and the degree of immunization. We relate our results to a three-phase model describing tumor evolution in living organisms with an intact immune system.