Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Χαλικιας Γεωργιος,αναπληρωτης καθηγητης
Καλογεροπουλος Γρηγορης,ομοτιμος καθηγητης
Αλικακος Νικολαος,Καθηγητης
Original Title:
A mathematical model for breast cancer and optimal controlled therapies
Translated title:
A mathematical model for breast cancer and optimal controlled therapies
Summary:
In this master thesis we describe a mathematical model for breast cancer based on a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet. Analytic methods are being used to examine the stability of the model. Moreover we seek out the sufficient conditions for the parameter values to test cancer tumor persistence when different therapies are being applied. Optimal control theory is being used adapted to verify the optimal drug dosage as an input control of the system therapies,in order to minimize the population of tumor cells under different control combinations of cure strategies utalizing the maximum principle of Pontryagin. Last but not least, numerical simulations verify the theoritical results for both the non linear and the linear model using LQR and H∞ algorithms.
Main subject category:
Science
Keywords:
Maths,biology,Cancer,simulation,optimal control
