Control and Optimization
Alireza Fakharzadeh Jahromi; Mahin Azizi Karachi; Hajar Alimorad
Abstract
Cancer is a class of diseases characterized by uncontrolled cell growth that affects immune cells. There are several treatment options available, including surgery, chemotherapy, hormonal therapy, radiation therapy, targeted therapy, and ...
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Cancer is a class of diseases characterized by uncontrolled cell growth that affects immune cells. There are several treatment options available, including surgery, chemotherapy, hormonal therapy, radiation therapy, targeted therapy, and palliative care. Among these, chemotherapy is one of the most widely used and recognized methods. This paper presents a novel model designed to control cancer cell growth based on a system of nonlinear fractional differential equations with delay in chemotherapy. The model focuses on the competition between tumor and immune cells to minimize the number of tumor cells and determine the optimal dosage of the administered drug. It can simulate various scenarios and predict the outcomes of different chemotherapy regimens. By employing discretization and the Grunwald-Letnikov method, we aim to gain insights into why some patients respond well to chemotherapy while others do not. The results may also help identify potential drug targets and optimize existing treatments.
Hajar Alimorad; Alireza Fakharzadeh Jahromi
Abstract
In this paper, we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset of 3-dimensional space. The place of sensor is modeled by a subdomain of this region ...
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In this paper, we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset of 3-dimensional space. The place of sensor is modeled by a subdomain of this region of a given measure. By using an approach based on the embedding process, first, the system is formulated in variational form; then, by defining two positive Radon measures, the problem is represented in a space of measures. In this way, the shape design problem is turned into an infinite linear problem whose solution is guaranteed. In this step, the optimal solution (optimal control, optimal region, and optimal energy) is identified by a 2-phase optimization search technique applying two subsequent approximation steps. Moreover, some numerical simulations are given to compare this new method with other methods.
