Mathematical Modeling And Analysis Of Prostate Cancer Treatment

Prostate cancer is a type of malignancy that mostly affects older men.This malignant tumor is concentrated in prostate cells but sometimes spreads to surrounding tissues and other parts of the body.This type of cancer usually develops slowly and could be completely eliminated or successfully treated after diagnosis,but unfortunately it could be fatal.Several mathematical works have been focused on mathematical biology and medicine to give a new insight into treatment strategy.Therefore,the purpose of this dissertation is to study the evolution and the development of prostate cancer and to reveal the outcomes of different treatment modalities.In Chapter 1,biological background of prostate cancer,the existent treatments,important advances in modeling prostate cancer that are related to our work are introduced.Some mathematics terminologies and theorems that are used in this dissertation are stated.Meanwhile,the main contributions are briefly indicated.In Chapter 2,a new stochastic model of prostate cancer under continuous androgen suppression therapy is investigated to show the effects of noises,different competition intensities and dosage amount on treatment strategy.Threshold conditions between extinction and persistence in mean for the stochastic system are obtained where noises play an important role in persistence and eradication of tumor cells.Sufficient conditions for the existence of an ergodic stationary distribution are established.Furthermore,the optimal treatment is approximated by using numerical simulations.Finally,sufficient conditions on the existence of periodic solutions in case of the periodic effect of treatment are derived.The analysis of this model suggests that a medicament that overlap with the replication of tumor cells is advantageous for treatment with CAS therapy because of the similar effect of noise disturbances.In addition,the results motivate physicians to find a drug that would reduce the activity of resistance cells in order to prevent relapse and reduce the severity of cancer if it can not be cured.Chapter 3 is devoted to study a mathematical ODE model of prostate cancer treated by immunotherapy.First,we focused on the bifurcation analysis of the interaction between resistance cells and immune cells without vaccines by using analytic method.Then,to show the influence of the vaccines(immunotherapy)and immune response efficiency on the extinction and cyclic behavior of resistance cells,bifurcation analysis is performed by using numerical method.It is found that the model exhibits complex behaviors such as a saddle-node bifurcation,Hopf bifurcation,Bogdanov-Takens bifurcation and generalized Hopf bifurcation.Moreover,it is shown that the vaccines amount and T-cells killing efficiency of tumor cells have a significant effect on tumor cells behavior where the use of continuous dendritic cell vaccines to enhance the body's immune system with a high vaccine amount can keep tumor cells in a low level or at least avoid the relapse and lead to the periodic behavior of resistance cells in case when a cure cannot be achieved.Moreover,the outcome of the therapy may depend on the initial state of tumor cells in case of the existence of two limit cycles.In Chapter 4,brief conclusion and some future works and directions are proposed in the hope of giving a deeper insight into prostate treatment strategy and then participate on improving treatment modalities and the patient quality of life.