Mathematical study and asymptotic analysis of a model for tumor drug resistance
Résumé
In this paper we study a partial differential equations model for tumor drug resistance.
The aim is to take two different treatments into account: a specific tyrosine kinase inhibitor (TKI)
targeted therapy, with a cytotoxic effect, that induces direct cell death, and a multi-targeted TKI,
with both cytotoxic and anti-angiogenic effect, which prevents the creation of new blood vessels.
The model is based on mass balance equations on cell densities coupled with a diffusion equation
for the nutrients and oxygen concentration. We also consider a necrotic phase composed of dead
cells, which are eliminated at a rate 1/τ . We first prove that, for any non-negative τ , the model
is well-posed and in a second part we study the asymptotic behavior for small τ . Such a result
is of great interest for the modeling, since it provides a family of τ -dependent models which is
continuous with respect to τ
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