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Stability Analysis of a Fractional-Order Differential Equation System of a GBM-IS Interaction Depending on the Density |
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PP: 1021-1028 |
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Author(s) |
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Fatma Bozkurt,
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Abstract |
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In this paper, fractional-order is introduced into the interaction model between GBM and IS. GBM (Glioblastoma
Multiforme) is a brain tumor, that has a monoclonal origin and produces after reaching a specific density another tumor with different
growth rate and treatment susceptibilities. The IS cells are also divided into two populations, namely, the macrophages and the activated
macrophages. Hence, this model show two conversions, the conversion from sensitive tumor cell to resistant tumor cell and the
conversion from macrophages to active macrophages, and an interaction between the tumor cell and the macrophages. In this work,
it is shown that the model possesses non-negative solutions. Furthermore, the stability, existence and uniqueness were studied. To
investigate the conditions for an extinction of the tumor cells, Allee threshold is considered. Numerical simulations will give a detailed
description of the behavior of the constructed models at the end of the paper. |
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