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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2013-03-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.787 |
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| Summary: | 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. |
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| ISSN: | 1551-0018 |