Optimal Control Analysis of a Mathematical Model for Breast Cancer

Abstract

In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analysis was carried out using varieties of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs ketogenic diet and cancer emission when anti-cancer drugs, immune-booster, ketogenic diet are included were established. Furthermore, optimal control theory is applied to find out the optimal drug adjustment as an input control of the system therapies to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin's Maximum Principle. Numerical simulations were presented to validate our theoretical results.

Crosstalk between HER2 and PD-1/PD-L1 in Breast Cancer: From Clinical Applications to Mathematical Models

“…Another advantage of representing cancer mechanisms in terms of mathematical models is that it enables easy design and implementation of algorithms for optimizing drug dose and effective treatment schedules [35,186]. Even though many such optimization results are reported for various cancers [31,158], only a few studies are reported specifically for BC [36]. Even though many such optimization results are reported for various cancers [31,35,158,186], only a few studies are reported specifically for BC [36].…”

“…The data flow arrows in Figure 1 indicate the use of experimental data from preclinical and clinical trials to devise mathematical models. On the other hand, the results obtained from theoretical analysis using mathematical models (e.g., tumor doubling time, optimal drug dose, predicted tumor volume, estimated time for relapse of disease) are used to optimize the clinical experiment and proposed therapeutic strategy [31,[35][36][37][38]. Specifically, mathematical models can be used to analyze drug distribution (pharmacokinetics), drug response (pharmacodynamics) to monotherapy and combination therapy, development of drug resistance, and effect of drug toxicity related to cancer treatment [39,40].…”

Radiative Microwave Heating of Hyperthermia Therapy on Breast Cancer in a Porous Medium

“…Additionally, the benefit of utilizing porous media theory in modeling bioheat transfer due to fewer assumptions as compared to different established bioheat transfer models are stressed by [2,[28][29][30][31][32][33].…”

“…If not stopped, it may spread to other parts of the body through the lymphatic system or blood stream. It is caused by both internal (DNA damage, hormones imbalanced) and external (environmental such as tobacco smoking, alcoholic consumption, chemical substances etc) factors [2]. In this study, the focus shall be on female breast cancer.…”

Lie Symmetry and Painlevé Test for the SIRD Model

“…The model divides the total population into three different classes: The susceptible class, S, are those who can get infected with the disease; the infective class, I, are those who can spread the disease after getting infected; the removed class, R, are those individuals who recovered from the disease, resistant or sequestered while waiting for recovery; and the death class, D, are those who die from the disease. Most of the infantile viruses, essentially measles, have a removed and death class [14]. The model flow diagram which represented the disease is given by…”