Control Strategies for Cancer Therapy

Padmanabhan, Regina; Meskin, Nader; Moustafa, Ala‐Eddin Al

doi:10.1007/978-981-15-8640-8_10

Cited by 2 publications

(7 citation statements)

References 134 publications

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“…However, it requires the maximum treatment capacity of the community to be effective. This leads to an improvement of both proportional and constant treatments, as proposed in [47][48][49][50][51]. Equations (3.2) and (3.3) can be rewritten as follows:…”

Section: Treatment Rate Analysismentioning

confidence: 99%

“…Recently, Padmanabhan et al [50] proposed an optimization technique to solve the general form of nonlinear fractional dynamical systems optimal control problems (NFOCP), ruled by combined conditions. They developed an NFOCP-based model for cancer treatment that included the population of fat cells, immune cells, normal cells, tumor cells, and concentrations of chemotherapeutic and immunotherapeutic drugs.…”

Section: Optimal Control Theory In Cancer Treatmentmentioning

confidence: 99%

“…This is because any infected individuals introduced into the population will eventually lead the system back to the cell‐free equilibrium where

c_{i} = 0

. Conversely, for reproduction numbers greater than 1, the

{CCAE}_{i}

phase transitions from stable to unstable, resulting in unique endemic equilibria that are locally asymptotically stable [34, 41–50]. To establish the stability and existence of these endemic equilibria for our proposed models, we compute the values of

η

and

β_{2}

based on the reproduction equations as follows:

η = \frac{α_{2} - α_{1} β_{2} K_{1} {scriptR}_{1, 0}}{{scriptR}_{1, 0} - θ β_{2} K_{1}}, β_{2} = \frac{α_{2}}{K_{1} α_{1} {scriptR}_{2, 0}},

…”

Section: Mathematical Model For the Coexistence Of Healthy And Cancer...mentioning

confidence: 99%

“…According to sources [47–51], a constant treatment rate is achieved when the infection reproduction number is high. The modified treatment rate, presented in [50], is as follows:

f (c) = \{\begin{matrix} γc; 0 \leq c \leq c_{0}, \\ γ c_{0}; c > c_{0}, \end{matrix}

…”

Section: Mathematical Model For the Coexistence Of Healthy And Cancer...mentioning

confidence: 99%

“…However, it requires the maximum treatment capacity of the community to be effective. This leads to an improvement of both proportional and constant treatments, as proposed in [47–51]. Equations () and () can be rewritten as follows:

\{\begin{matrix} \frac{dh (t)}{italicdt} = K_{1} (α_{1} - θη) (1 - \frac{h (t)}{K_{1}}) - β_{1} \frac{K_{1} (α_{1} - θη)}{α_{1}} c (t) - θηh (t) + f (c), \\ \frac{dc (t)}{italicdt} = α_{2} c (t) - β_{2} K_{1} (α_{1} - θη) c (t) - ηc (t) - f (c), \end{matrix}

and

\{\begin{matrix} \frac{dh (t)}{italicdt} = α_{1} K_{1} (1 - \frac{h (t)}{K_{1}}) - β_{1} K_{1} c (t) + f (c), \\ \frac{dc (t)}{italicdt} = α_{2} c (t) - β_{2} K_{1} c (t) - f (c) . \end{matrix}

…”

Section: Mathematical Model For the Coexistence Of Healthy And Cancer...mentioning

confidence: 99%

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On the role of optimization in the cancer treatment by radiation therapy (RT)

Chaharborj

Yarahmadian

2023

Math Methods in App Sciences

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In this paper, we present a mathematical model that analyzes cancer treatment via radiotherapy and proposes ways to control its progression. To identify preventive measures for cancer in its early stages, scientists have studied both risk factors and protective factors. In our model, we consider the disease‐free equilibrium points, namely, the trivial equilibrium (TE), healthy cell absenteeism equilibrium (HCAE), cancer cell absenteeism equilibrium (CCAE), and cancer cell incidence equilibrium (CCIE). We use nonlinear analysis techniques and the spectral radius method to study the stability and instability of systems. Since the reproduction number plays a critical role in stability analysis, we use the spectral radius method to evaluate it. We have also added a control function to the model to enhance it by including interactions between healthy and cancer cells. Optimization techniques are used to identify the limitations and needs of the problem and derive the best solutions to control the tumor. We conduct sensitivity analysis with respect to various parameters to study the model's robustness. To validate our methods and results, we provide simulations and numerical analysis.

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Section: Treatment Rate Analysismentioning

confidence: 99%

Section: Optimal Control Theory In Cancer Treatmentmentioning

confidence: 99%

“…This is because any infected individuals introduced into the population will eventually lead the system back to the cell‐free equilibrium where

c_{i} = 0

. Conversely, for reproduction numbers greater than 1, the

{CCAE}_{i}

η

and

β_{2}

based on the reproduction equations as follows:

η = \frac{α_{2} - α_{1} β_{2} K_{1} {scriptR}_{1, 0}}{{scriptR}_{1, 0} - θ β_{2} K_{1}}, β_{2} = \frac{α_{2}}{K_{1} α_{1} {scriptR}_{2, 0}},

…”

Section: Mathematical Model For the Coexistence Of Healthy And Cancer...mentioning

confidence: 99%

“…According to sources [47–51], a constant treatment rate is achieved when the infection reproduction number is high. The modified treatment rate, presented in [50], is as follows:

f (c) = \{\begin{matrix} γc; 0 \leq c \leq c_{0}, \\ γ c_{0}; c > c_{0}, \end{matrix}

…”

Section: Mathematical Model For the Coexistence Of Healthy And Cancer...mentioning

confidence: 99%

“…However, it requires the maximum treatment capacity of the community to be effective. This leads to an improvement of both proportional and constant treatments, as proposed in [47–51]. Equations () and () can be rewritten as follows:

\{\begin{matrix} \frac{dh (t)}{italicdt} = K_{1} (α_{1} - θη) (1 - \frac{h (t)}{K_{1}}) - β_{1} \frac{K_{1} (α_{1} - θη)}{α_{1}} c (t) - θηh (t) + f (c), \\ \frac{dc (t)}{italicdt} = α_{2} c (t) - β_{2} K_{1} (α_{1} - θη) c (t) - ηc (t) - f (c), \end{matrix}

and

\{\begin{matrix} \frac{dh (t)}{italicdt} = α_{1} K_{1} (1 - \frac{h (t)}{K_{1}}) - β_{1} K_{1} c (t) + f (c), \\ \frac{dc (t)}{italicdt} = α_{2} c (t) - β_{2} K_{1} c (t) - f (c) . \end{matrix}

…”

Section: Mathematical Model For the Coexistence Of Healthy And Cancer...mentioning

confidence: 99%

See 3 more Smart Citations

On the role of optimization in the cancer treatment by radiation therapy (RT)

Chaharborj

Yarahmadian

2023

Math Methods in App Sciences

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Recent Advances in Molecular Mechanisms of Cancer Immunotherapy

Kciuk

Yahya

Mohamed

et al. 2023

Cancers

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Cancer is among the current leading causes of death worldwide, despite the novel advances that have been made toward its treatment, it is still considered a major public health concern. Considering both the serious impact of cancer on public health and the significant side effects and complications of conventional therapeutic options, the current strategies towards targeted cancer therapy must be enhanced to avoid undesired toxicity. Cancer immunotherapy has become preferable among researchers in recent years compared to conventional therapeutic options, such as chemotherapy, surgery, and radiotherapy. The understanding of how to control immune checkpoints, develop therapeutic cancer vaccines, genetically modify immune cells as well as enhance the activation of antitumor immune response led to the development of novel cancer treatments. In this review, we address recent advances in cancer immunotherapy molecular mechanisms. Different immunotherapeutic approaches are critically discussed, focusing on the challenges, potential risks, and prospects involving their use.

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Control Strategies for Cancer Therapy

Cited by 2 publications

References 134 publications

On the role of optimization in the cancer treatment by radiation therapy (RT)

On the role of optimization in the cancer treatment by radiation therapy (RT)

Recent Advances in Molecular Mechanisms of Cancer Immunotherapy

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