A non-local model for cancer stem cells and the tumor growth paradox
Iacopo Borsi, Antonio Fasano, Mario Primicerio, Thomas Hillen
The "tumor growth paradox" refers to the observation that incomplete
treatment of cancers can enhance their growth. As shown here and
elsewhere, the existence of cancer stem cells (CSC) can explain this
effect. CSC are less sensitive to treatments, hence any stress applied
to the tumor selects for CSC, thereby increasing the fitness of the
tumor.
In this paper we use a mathematical model to understand the role of CSC
in the progression of cancer. Our model is a rather general system of
integro-differential equations for tumor growth and tumor spread. Such a
model has never been analysed, and we prove results on local and global
existence of solutions, their uniqueness and their boundedness. We show
numerically that this model exhibits the tumor growth paradox for all
parameters tested. This effect becomes more relevant for small renewal
rate of the CSC.
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