声明
Chapter 1 Introduction
1.1 Background of prostate cancer and treatment
1.1.1 Hormone therapy
1.1.2 Immunotherapy
1.1.3 Further treatments
1.2 Literature review of mathematical models
1.3 Contributions
1.4 Background of stochastic noise and bifurcation theory
1.4.1 Stochastic differential equations
1.4.2 Bifurcation theory
Chapter 2 Sto chastic mo del of CAS therapy
2.1 Model formulation
2.2 Mathematical analysis
2.2.1 Existence and uniqueness of solution
2.2.2 Persistence in mean and extinction
2.2.3 Stationary distribution and ergodicity for system
2.3 Approximation of optimal treatment
2.4 Extension to periodic treatment
2.4.1 Qualitative results
2.4.2 Existence of periodic solutions
2.4.3 Numerical simulations
2.5 Conclusions
Chapter 3 Bifurcation in immunotherapy model
3.1 Mathematical model
3.2 Dynamics of model without immunotherapy
3.2.1 Equilibrium points and their stability
3.2.2 Bifurcation analysis
3.3 Bifurcation of model with immunotherapy
3.3.1 The effect of dendritic cells vaccines on tumor cells
3.3.2 Periodic behavior of tumor cells
3.4 Conclusions
Chapter 4 Discussions
参考文献
Academic papers completed and published during the Ph.D.
致谢
