Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions
Immunotherapy is one of the future treatments applicable in most cases of cancer including malignant cancer. Malignant cancer usually prevents some genes, e.g., p53 and pRb, from controlling the activation of the cell division and the cell apoptosis. In this paper, we consider the interactions among...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2021/5535447 |
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| author | Sulasri Suddin Fajar Adi-Kusumo Lina Aryati Gunardi |
| author_facet | Sulasri Suddin Fajar Adi-Kusumo Lina Aryati Gunardi |
| author_sort | Sulasri Suddin |
| collection | DOAJ |
| description | Immunotherapy is one of the future treatments applicable in most cases of cancer including malignant cancer. Malignant cancer usually prevents some genes, e.g., p53 and pRb, from controlling the activation of the cell division and the cell apoptosis. In this paper, we consider the interactions among the cancer cell population, the effector cell population that is a part of the immune system, and cytokines that can be used to stimulate the effector cells called the IL-2 compounds. These interactions depend on both time and spatial position of the cells in the tissue. Mathematically, the spatial movement of the cells is represented by the diffusion terms. We provide an analytical study for the constant equilibria of the reaction-diffusion system describing the above interactions, which show the initial behaviour of the tissue, and we conduct numerical simulation that shows the dynamics along the tissue that represent the immunotherapy effects. In this case, we also consider the steady-state conditions of the system that show the long-time behaviour of these interactions. |
| format | Article |
| id | doaj-art-b1549ad7072344bb951faa5ba5a9b936 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-b1549ad7072344bb951faa5ba5a9b9362025-02-03T05:45:22ZengWileyInternational Journal of Differential Equations1687-96431687-96512021-01-01202110.1155/2021/55354475535447Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ InteractionsSulasri Suddin0Fajar Adi-Kusumo1Lina Aryati2Gunardi3Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Yogyakarta, IndonesiaImmunotherapy is one of the future treatments applicable in most cases of cancer including malignant cancer. Malignant cancer usually prevents some genes, e.g., p53 and pRb, from controlling the activation of the cell division and the cell apoptosis. In this paper, we consider the interactions among the cancer cell population, the effector cell population that is a part of the immune system, and cytokines that can be used to stimulate the effector cells called the IL-2 compounds. These interactions depend on both time and spatial position of the cells in the tissue. Mathematically, the spatial movement of the cells is represented by the diffusion terms. We provide an analytical study for the constant equilibria of the reaction-diffusion system describing the above interactions, which show the initial behaviour of the tissue, and we conduct numerical simulation that shows the dynamics along the tissue that represent the immunotherapy effects. In this case, we also consider the steady-state conditions of the system that show the long-time behaviour of these interactions.http://dx.doi.org/10.1155/2021/5535447 |
| spellingShingle | Sulasri Suddin Fajar Adi-Kusumo Lina Aryati Gunardi Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions International Journal of Differential Equations |
| title | Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions |
| title_full | Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions |
| title_fullStr | Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions |
| title_full_unstemmed | Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions |
| title_short | Reaction-Diffusion on a Spatial Mathematical Model of Cancer Immunotherapy with Effector Cells and IL-2 Compounds’ Interactions |
| title_sort | reaction diffusion on a spatial mathematical model of cancer immunotherapy with effector cells and il 2 compounds interactions |
| url | http://dx.doi.org/10.1155/2021/5535447 |
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