On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth
In this paper, a mathematical model for chemotherapy that takestumor immune-system interactions into account is considered for astrongly targeted agent. We use a classical model originallyformulated by Stepanova, but replace exponential tumor growth with ageneralised logistic growth model function d...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.787 |
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| author | Urszula Ledzewicz Omeiza Olumoye Heinz Schättler |
| author_facet | Urszula Ledzewicz Omeiza Olumoye Heinz Schättler |
| author_sort | Urszula Ledzewicz |
| collection | DOAJ |
| description | In this paper, a mathematical model for chemotherapy that takestumor immune-system interactions into account is considered for astrongly targeted agent. We use a classical model originallyformulated by Stepanova, but replace exponential tumor growth with ageneralised logistic growth model function depending on a parameter$\nu$. This growth function interpolates between a Gompertzian model(in the limit $\nu\rightarrow0$) and an exponential model (in thelimit $\nu\rightarrow\infty$). The dynamics is multi-stable andequilibria and their stability will be investigated depending on theparameter $\nu$. Except for small values of $\nu$, the system hasboth an asymptotically stable microscopic (benign) equilibrium pointand an asymptotically stable macroscopic (malignant) equilibriumpoint. The corresponding regions of attraction are separated by thestable manifold of a saddle. The optimal control problem of movingan initial condition that lies in the malignant region into thebenign region is formulated and the structure of optimal singularcontrols is determined. |
| format | Article |
| id | doaj-art-9c913710c64740be9203ee2fd3c77f31 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9c913710c64740be9203ee2fd3c77f312025-01-24T02:26:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-03-0110378780210.3934/mbe.2013.10.787On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growthUrszula Ledzewicz0Omeiza Olumoye1Heinz Schättler2Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653In this paper, a mathematical model for chemotherapy that takestumor immune-system interactions into account is considered for astrongly targeted agent. We use a classical model originallyformulated by Stepanova, but replace exponential tumor growth with ageneralised logistic growth model function depending on a parameter$\nu$. This growth function interpolates between a Gompertzian model(in the limit $\nu\rightarrow0$) and an exponential model (in thelimit $\nu\rightarrow\infty$). The dynamics is multi-stable andequilibria and their stability will be investigated depending on theparameter $\nu$. Except for small values of $\nu$, the system hasboth an asymptotically stable microscopic (benign) equilibrium pointand an asymptotically stable macroscopic (malignant) equilibriumpoint. The corresponding regions of attraction are separated by thestable manifold of a saddle. The optimal control problem of movingan initial condition that lies in the malignant region into thebenign region is formulated and the structure of optimal singularcontrols is determined.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.787optimal controlgeneralized logistic growth.tumor immune system interactionstargeted chemotherapy |
| spellingShingle | Urszula Ledzewicz Omeiza Olumoye Heinz Schättler On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth Mathematical Biosciences and Engineering optimal control generalized logistic growth. tumor immune system interactions targeted chemotherapy |
| title | On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth |
| title_full | On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth |
| title_fullStr | On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth |
| title_full_unstemmed | On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth |
| title_short | On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth |
| title_sort | on optimal chemotherapy with a strongly targeted agent for a model of tumor immune system interactions with generalized logistic growth |
| topic | optimal control generalized logistic growth. tumor immune system interactions targeted chemotherapy |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.787 |
| work_keys_str_mv | AT urszulaledzewicz onoptimalchemotherapywithastronglytargetedagentforamodeloftumorimmunesysteminteractionswithgeneralizedlogisticgrowth AT omeizaolumoye onoptimalchemotherapywithastronglytargetedagentforamodeloftumorimmunesysteminteractionswithgeneralizedlogisticgrowth AT heinzschattler onoptimalchemotherapywithastronglytargetedagentforamodeloftumorimmunesysteminteractionswithgeneralizedlogisticgrowth |