Set-valued analysis of anti-angiogenic therapy and radiotherapy

MOUSTAFİD, Amine

doi:10.53391/mmnsa.2022.015

Cited by 3 publications

(4 citation statements)

References 30 publications

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“…1, is reversed to an upper exponential decreasing y(t) ≤ y 0 e −αt (11) with α > α 1 , towards null limit (7), see Fig. 2, by the therapy (v I (t), v M (t), h m (t)) = u(t, x) solution to the minimization problem (20), which is numerically solved in the Section 4 by Uzawa method (26-27) of parameter (λ, σ), to get numerical solution (y, x) of discretized model (25) by Euler method of step h, see Fig. 3.…”

Section: Discussionmentioning

confidence: 99%

“…Remark 3. The variant of an infeasible interior-point algorithm presented in [48], may be also used to solve the problem of minimization (20).…”

Section: Numerical Modelmentioning

confidence: 99%

“…[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%

“…In this paper we propose to extend the set-valued method of papers [18][19][20][21] into non autonomous model of three mixed therapies of immunotherapy, chemotherapy, and radiotherapy. Section 2 presents the model and states the associated control problem in the viability form.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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: Discussionmentioning

confidence: 99%

“…Remark 3. The variant of an infeasible interior-point algorithm presented in [48], may be also used to solve the problem of minimization (20).…”

Section: Numerical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

MOUSTAFİD¹

2023

IJIAM

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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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Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

Fatima

Yavuz

Rahman

et al. 2023

MBE

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<abstract><p>Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number ($ \mathcal{R}_{0} $) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of $ \mathcal{R}_{0} $ to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time-dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.</p></abstract>

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Set-valued analysis of anti-angiogenic therapy and radiotherapy

Cited by 3 publications

References 30 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

Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

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