Mathematical and Numerical Analysis of Chemotherapy Resistance in Tumors: Modeling Integrating Darwinian, Lamarckian, and Microvesicle-Mediated Mechanisms with the WENO5 Scheme

Abstract

We develop a mathematical model to describe the spatio-temporal evolution of chemotherapy-sensitive and chemotherapy-resistant tumor cells. The model incorporates three distinct mechanisms driving resistance after drug administration: Darwinian selection, Lamarckian induction (LI), and the transfer of resistance via microvesicles (MVs) from resistant to sensitive cells, akin to the spread of infectious agents. We establish the existence and uniqueness of solutions using a fixed-point method, and we prove two key qualitative properties: the positivity of cell densities and the conservation of total mass under a saturation assumption, using the maximum principle. We also investigate the asymptotic behavior of the model as the characteristic evacuation time of necrosis tends to zero. Numerical simulations are performed to evaluate the individual and combined effects of MV transfer and LI on tumor progression and treatment resistance. Our findings reveal that these mechanisms substantially enhance resistance, leading to accelerated tumor growth. Overall, the proposed model offers a robust framework to understand the dynamics of resistance in tumor populations and may inform the design of more effective, multi-targeted chemotherapy strategies.

Keywords

Tumor modeling / Chemotherapy resistance / Microvesicles (MVs) transfer / Lamarckian induction (LI) / Fixed point / Twin-WENO5 / 35M13 / 65M22

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