Analysis of a cancer dormancy model and control of immuno-therapy
The goal of this paper is to analyze a model of cancer-immune system interactions from [16], and to show how the introduction of control in this model can dramatically improve the hypothetical patient response and in effect prevent the cancer from growing. We examine all the equilibrium points of...
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AIMS Press
2015-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1037 |
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| author | Ben Sheller Domenico D'Alessandro |
| author_facet | Ben Sheller Domenico D'Alessandro |
| author_sort | Ben Sheller |
| collection | DOAJ |
| description | The goal of this paper is to analyze a model of cancer-immune system interactions from [16], and to show how the introduction of control in this model can dramatically improve the hypothetical patient response and in effect prevent the cancer from growing. We examine all the equilibrium points of the model and classify them according to their stability properties. We identify an equilibrium point corresponding to a survivable amount of cancer cells which are exactly balanced by the immune response. This situation corresponds to cancer dormancy. By using Lyapunov stability theory we estimate the region of attraction of this equilibrium and propose two control laws which are able to stabilize the system effectively, improving the results of [16]. Ultimately, the analysis presented in this paper reveals that a slower, continuous introduction of antibodies over a short time scale, as opposed to mere inoculation, may lead to more efficient and safer treatments. |
| format | Article |
| id | doaj-art-f7bf8667f544462fbf8dccf0d0f1ee52 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f7bf8667f544462fbf8dccf0d0f1ee522025-01-24T02:33:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-05-011251037105310.3934/mbe.2015.12.1037Analysis of a cancer dormancy model and control of immuno-therapyBen Sheller0Domenico D'Alessandro1Department of Mathematics, Iowa State University, Ames, IA 50011Department of Mathematics, Iowa State University, Ames, IA 50011The goal of this paper is to analyze a model of cancer-immune system interactions from [16], and to show how the introduction of control in this model can dramatically improve the hypothetical patient response and in effect prevent the cancer from growing. We examine all the equilibrium points of the model and classify them according to their stability properties. We identify an equilibrium point corresponding to a survivable amount of cancer cells which are exactly balanced by the immune response. This situation corresponds to cancer dormancy. By using Lyapunov stability theory we estimate the region of attraction of this equilibrium and propose two control laws which are able to stabilize the system effectively, improving the results of [16]. Ultimately, the analysis presented in this paper reveals that a slower, continuous introduction of antibodies over a short time scale, as opposed to mere inoculation, may lead to more efficient and safer treatments.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1037lyapunov stability.modeling of immuno-therapyapplication of control theory to cancer therapy |
| spellingShingle | Ben Sheller Domenico D'Alessandro Analysis of a cancer dormancy model and control of immuno-therapy Mathematical Biosciences and Engineering lyapunov stability. modeling of immuno-therapy application of control theory to cancer therapy |
| title | Analysis of a cancer dormancy model and control of immuno-therapy |
| title_full | Analysis of a cancer dormancy model and control of immuno-therapy |
| title_fullStr | Analysis of a cancer dormancy model and control of immuno-therapy |
| title_full_unstemmed | Analysis of a cancer dormancy model and control of immuno-therapy |
| title_short | Analysis of a cancer dormancy model and control of immuno-therapy |
| title_sort | analysis of a cancer dormancy model and control of immuno therapy |
| topic | lyapunov stability. modeling of immuno-therapy application of control theory to cancer therapy |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1037 |
| work_keys_str_mv | AT bensheller analysisofacancerdormancymodelandcontrolofimmunotherapy AT domenicodalessandro analysisofacancerdormancymodelandcontrolofimmunotherapy |