Article
An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy
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Abstract
We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the influx of chemotherapy is restricted to a limited region of the tissue, mimicking a blood vessel passing transversely. We provide results on the existence and uniqueness of the model solution and numerical simulations illustrating different model behaviors.
Keywords
Nonlinear system, existence of solutions, tumor growth, chemotherapeutic drug, Primary: 35Q92, 35K45, 35K57, Secundary: 92C60, 92C50, 92C37
Citation
de Araujo, A. L. A., Fassoni, A. C., & Salvino, L. F. (2020). An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy. Applied Mathematics and Nonlinear Sciences, 5(2), 185–204. https://doi.org/10.2478/amns.2020.2.00037
A. L. A. de Araujo, A. C. Fassoni and L. F. Salvino, “An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, pp. 185–204, 2020, doi: 10.2478/amns.2020.2.00037.
de Araujo ALA, Fassoni AC, Salvino LF. An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy. Applied Mathematics and Nonlinear Sciences. 2020;5(2):185–204. doi:10.2478/amns.2020.2.00037.
de Araujo, A. L. A., Fassoni, A. C. and Salvino, L. F. (2020), ‘An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy’, Applied Mathematics and Nonlinear Sciences, 5(2), pp. 185–204. Available at: https://doi.org/10.2478/amns.2020.2.00037.
de Araujo, Anderson L. A., et al. “An Analysis of a Mathematical Model Describing the Growth of a Tumor Treated with Chemotherapy.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, 2020, pp. 185–204. https://doi.org/10.2478/amns.2020.2.00037.
de Araujo, Anderson L. A., Artur C. Fassoni, and Luís F. Salvino. “An Analysis of a Mathematical Model Describing the Growth of a Tumor Treated with Chemotherapy.” Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 185–204. https://doi.org/10.2478/amns.2020.2.00037.
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Published by: Engineering Journals
