Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression
International Journal of Systems Science and Applied Mathematics
Volume 4, Issue 1, March 2019, Pages: 1-12
Received: Jan. 31, 2019; Accepted: Mar. 18, 2019; Published: Apr. 3, 2019
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Author
Kodwo Annan, School of Science and Technology, Georgia Gwinnett College, Lawrenceville, USA
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Abstract
Mathematical model that allowed qualitative and quantitative description of the interactions between the host immune system, breast cancer cells, and a cancer vaccine was presented with a system of differential equations. Key immune components used in the vaccine were cytotoxic T lymphocytes (CTLs), macrophages, Natural Killer (NK) and helper T cells. The parameters of the model were based on experimental and clinical results from published articles. MATLAB software tool was used to generate data from the model and results were analyzed and discussed. Findings supported clinical studies that maximum immune activation was needed to reduce the cancer cells. Thus, for a given breast cancer growth rate, there was an optimal activation that maximized the response of the immune system. It was also observed that given a sufficiently high rate of CTLs, natural killer, or helper T cells infiltration resulted in significant tumor elimination. However, varying CTLs and Macrophages activation rates caused a chaotic behavior of the tumor. Thus, optimizing large M1:M2 ratios verses large/small numbers of tumor-infiltrating macrophages on long term patient survival were necessary in improving breast cancer therapies.
Keywords
Breast Cancer, Immune System, Mathematical Model
To cite this article
Kodwo Annan, Modeling Immune-Mediated Activations and Interactions in Breast Cancer Progression, International Journal of Systems Science and Applied Mathematics. Vol. 4, No. 1, 2019, pp. 1-12. doi: 10.11648/j.ijssam.20190401.11
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Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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