A model describing the growth and the size distribution of multiple metastatic tumors

Anne Devys (1) , Thierry Goudon (1) , Pauline Lafitte (1)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids

Cancer is one of the greatest killers in the world, particularly in western countries. A great effort from medical research is devoted to cancer and mathematical modeling must be consider as an additional tool for the physicians and biologists to understand cancermechanisms and to determine the adapted treatments. Metastasis make all the seriousness of cancer. In 2000, Iwata et al. [9] proposed a model which describes the evolution of an untreated metastatic tumors population. We provide here a mathematical analysis of this model which brings us to the determination of a Malthusian rate characterizing the population exponential growth. We provide as well a numerical analysis of the PDE given by the model.

Mots clés: McKendrick-Von Foerster equation; relative entropy; asymptotic behavior; WENO scheme; metastatic tumors

Domaines: Equations aux dérivées partielles [math.AP]

Anne Devys, Thierry Goudon, Pauline Lafitte. A model describing the growth and the size distribution of multiple metastatic tumors. Discrete and Continuous Dynamical Systems - Series B, 2009, 12 (4), pp.731-767. ⟨10.3934/dcdsb.2009.12.731⟩. ⟨inria-00351489⟩