| Abstract: |
| Understanding the emergence of chemotherapy resistance in cancer patients, whether driven by Darwinian evolution, gene expression changes, or the transfer of microvesicles from resistant to sensitive cells, is crucial as it significantly impacts treatment outcomes by promoting the survival and spread of resistant cells. We have developed a mathematical model to describe the evolution of tumor cells that are either sensitive or resistant to chemotherapy and to make it more realistic by including a separate equation for the number of microvesicles. This model accounts for three resistance mechanisms: Darwinian selection, Lamarckian induction, and resistance via microvesicle transfer, mimicking infectious spread. Our analysis identifies three key threshold parameters that determine the stability and existence of different equilibria within the system. We provide a comprehensive description of the global dynamics, including the existence of global attractors, depending on these threshold values. Additionally, we explore the effects of varying drug concentrations and characterize potential bifurcation sequences that lead to either successful treatment or therapeutic failure. Lastly, we identify the factor that exerts the most significant influence on cancer cell growth. |
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