scholarly journals A fractional-order delay differential model with optimal control for cancer treatment based on synergy between anti-angiogenic and immune cell therapies

2020 ◽  
Vol 13 (9) ◽  
pp. 2403-2424 ◽  
Author(s):  
Nasser Sweilam ◽  
◽  
Fathalla Rihan ◽  
Seham AL-Mekhlafi ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Cancer Treatment ◽  
Fractional Order ◽  
Immune Cell ◽  
Differential Model ◽  
Cell Therapies ◽  
Delay Differential

scholarly journals Delay Differential Model for Tumour-Immune System With Chemo-therapy and Optimal Control

2020 ◽  
Vol 31 ◽  
pp. 04003
Author(s):  
Fathalla A. Rihan ◽  
Bassel F. Rihan
Keyword(s):  
Optimal Control ◽  
Carrying Capacity ◽  
Tumour Cells ◽  
Chemotherapy Treatment ◽  
Control Variables ◽  
Differential Model ◽  
Effector Cells ◽  
Days Of Therapy ◽  
Delay Differential ◽  
Optimal Treatment Strategy

In this paper, we present a mathematical model of tumour-immune interactions in presence of chemotherapy treatment. The model is governed by a system of delay differential equations with optimal control variables. The control variables are included to justify the best strategy of treatments with minimum side effects, by reducing the production of new tumour cells and keeping the number of normal cells above the average of its carrying capacity. Existence of optimality and optimality conditions are also proved. The numerical simulations show that the optimal treatment strategy reduces the load of tumour cells and increases the effector cells after few days of therapy.

scholarly journals Delay Differential Model for Tumour-Immune Response with Chemoimmunotherapy and Optimal Control

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
F. A. Rihan ◽  
D. H. Abdelrahman ◽  
F. Al-Maskari ◽  
F. Ibrahim ◽  
M. A. Abdeen
Keyword(s):  
Optimal Control ◽  
Immune Response ◽  
Treatment Strategies ◽  
Tumour Cells ◽  
Optimal Controls ◽  
Control Pair ◽  
Differential Model ◽  
Effector Cells ◽  
Days Of Therapy ◽  
Delay Differential

We present a delay differential model with optimal control that describes the interactions of the tumour cells and immune response cells with external therapy. The intracellular delay is incorporated into the model to justify the time required to stimulate the effector cells. The optimal control variables are incorporated to identify the best treatment strategy with minimum side effects by blocking the production of new tumour cells and keeping the number of normal cells above 75% of its carrying capacity. Existence of the optimal control pair and optimality system are established. Pontryagin’s maximum principle is applicable to characterize the optimal controls. The model displays a tumour-free steady state and up to three coexisting steady states. The numerical results show that the optimal treatment strategies reduce the tumour cells load and increase the effector cells after a few days of therapy. The performance of combination therapy protocol of immunochemotherapy is better than the standard protocol of chemotherapy alone.

scholarly journals The Role of Cancer-Associated Fibroblasts in Tumor Progression

Cancers ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1399
Author(s):  
Rushikesh S. Joshi ◽  
Samanvi S. Kanugula ◽  
Sweta Sudhir ◽  
Matheus P. Pereira ◽  
Saket Jain ◽  
...  
Keyword(s):  
Cancer Treatment ◽  
Tumor Progression ◽  
Cancer Progression ◽  
Immune Cell ◽  
Systemic Disease ◽  
Genomic Medicine ◽  
Therapeutic Targets ◽  
Therapy Resistance ◽  
Cancer Associated Fibroblasts ◽  
Breast Cancers

In the era of genomic medicine, cancer treatment has become more personalized as novel therapeutic targets and pathways are identified. Research over the past decade has shown the increasing importance of how the tumor microenvironment (TME) and the extracellular matrix (ECM), which is a major structural component of the TME, regulate oncogenic functions including tumor progression, metastasis, angiogenesis, therapy resistance, and immune cell modulation, amongst others. Within the TME, cancer-associated fibroblasts (CAFs) have been identified in several systemic cancers as critical regulators of the malignant cancer phenotype. This review of the literature comprehensively profiles the roles of CAFs implicated in gastrointestinal, endocrine, head and neck, skin, genitourinary, lung, and breast cancers. The ubiquitous presence of CAFs highlights their significance as modulators of cancer progression and has led to the subsequent characterization of potential therapeutic targets, which may help advance the cancer treatment paradigm to determine the next generation of cancer therapy. The aim of this review is to provide a detailed overview of the key roles that CAFs play in the scope of systemic disease, the mechanisms by which they enhance protumoral effects, and the primary CAF-related markers that may offer potential targets for novel therapeutics.

Implementation of fractional optimal control problems in real-world applications

2020 ◽  
Vol 23 (6) ◽  
pp. 1783-1796
Author(s):  
Neelam Singha
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Necessary Optimality Conditions ◽  
Order Model ◽  
Fractional Optimal Control ◽  
Adomian Decomposition ◽  
Real World Applications ◽  
Fractional Optimal Control Problems ◽  
And Control

Abstract In this article, we aim to analyze a mathematical model of tumor growth as a problem of fractional optimal control. The considered fractional-order model describes the interaction of effector-immune cells and tumor cells, including combined chemo-immunotherapy. We deduce the necessary optimality conditions together with implementing the Adomian decomposition method on the suggested fractional-order optimal control problem. The key motive is to perform numerical simulations that shall facilitate us in understanding the behavior of state and control variables. Further, the graphical interpretation of solutions effectively validates the applicability of the present analysis to investigate the growth of cancer cells in the presence of medical treatment.

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