Set-Valued Control of Cancer by Combination Chemotherapy

MOUSTAFİD, Amine

doi:10.33187/jmsm.1069549

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…[17] Checks the controllability and observability for a mathematical model of immunotherapy and chemotherapy for cancer. [18] Uses set-valued analysis to approach the problem of decreasing and asymptotically stabilizing tumor cells, by anti-angiogenic therapy combined with radiotherapy, as well as in in [19] by tumor-immune with chemotherapy, so as in [20,21] by anti-angiogenic therapy with chemotherapy, while in [22] chemotherapy is used alone. [23] Studies the optimal effects of immuno-chemotherapy in the presence of gene therapy.…”

Section: Introductionmentioning

confidence: 99%

Viability control of chemo-immunotherapy and radiotherapy by set-valued analysis

MOUSTAFİD¹

2023

IJIAM

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In this paper we set-valued analyze the problem of asymptotic stabilizing the tumor size. A mathematical model of exponential tumor growing caused by carcinogenic substance is considered, with chemotherapy, immunotherapy, and radiotherapy effects. We control the model to be viable in therapeutic domains, and reverse the exponential growing of the tumor size. The obtained controls derive from the derivative cone of therapeutic domains as solution of minimizing problem.

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Section: Introductionmentioning

confidence: 99%

Viability control of chemo-immunotherapy and radiotherapy by set-valued analysis

MOUSTAFİD¹

2023

IJIAM

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“…The originality of this paper is that the set-valued methods developed to feedback stabilize the tumor density u(t), u(t) → 0, when t → ∞, subject to the odes [15,16,17]…”

Section: Introductionmentioning

confidence: 99%

Set-Valued Stabilization of Reaction-Diffusion Model by Chemotherapy and or Radiotherapy

MOUSTAFİD

2023

Fundamental Journal of Mathematics and Applications

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This paper aims to control partial differential equations, modeling cancer chemotherapy and or radiotherapy, so in order to asymptotically stabilize the tumor density. Viability kernel of general model on set of initial condition is used to solve the control problem, and characterize the control solution as regulation law of regulation map. Three models from the literature are considered to simulate the results. The first model includes chemotherapy effect on logistic tumor proliferation, while the second one demonstrates radiotherapy effect on exponential tumor increasing, whereas the third one models the effects of the combination of chemotherapy and radiotherapy on Gompertzian tumor growth.

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Cancer Modeling by Fractional Derivative Equation and Chemotherapy Stabilizing

Moustafid

2024

Communications in Advanced Mathematical Sciences

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This paper discusses the theme of cancer modeling and the problem of control by treatments. We model the cancer cells growth by fractional derivative equation and we stabilize their concentration by chemotherapy. The considered model will be converted into simple partial derivative equation and associated with a viability problem. We use the set-valued analysis to make viable the converted model by regulation law of regulation map. Applied chemotherapy concentration on cancer cells concentration follows the regulation law.

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Set-Valued Control of Cancer by Combination Chemotherapy

Cited by 3 publications

References 15 publications

Viability control of chemo-immunotherapy and radiotherapy by set-valued analysis

Viability control of chemo-immunotherapy and radiotherapy by set-valued analysis

Set-Valued Stabilization of Reaction-Diffusion Model by Chemotherapy and or Radiotherapy

Cancer Modeling by Fractional Derivative Equation and Chemotherapy Stabilizing

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