1 Introduction
1.1 First-order 1-Compartment Model (Extravascular Administration)
1.2 First-order 2-Compartment Model (Intravenous Dose)
1.3 Pontryagins Principle
1.3.1 Hamiltonian
1.3.2 Pontryagins Maximum (or Minimum) Principle
1.4 White Noise
1.5 Stochastic Differential Equations (SDEs)
1.5.1 The Concept of SDEs
1.5.2 Stability of the SDEs
1.6 Magnus Expansion
1.6.1 Bernoulli Number
1.6.2 Magnus Approach and Its Interpretation
1.7 Gronwall Lemma
2 Using Optimal Control Theory to Study the First Order Compartment Models
2.1 Using Optimal Control Theory to Study the First-order 1-Compartment Model
2.2 Using Optimal Control Theory to Study the First-order 2-Compartment Model
3 The First-order Compartment Stochastic Models
3.1 The First-order 1-Compartment Stochastic Model
3.2 The First-order 2-Compartment Stochastic Model
4 Qualitative Analysis of the Stochastic Models
4.1 Qualitative Analysis of the First-order 1-Compartment Stochastic Model
4.2 Qualitative Analysis of the First-order 2-Compartment Stochastic Model
5 Quantitative Analysis of the Models
5.1 Quantitative Analysis of the First-order 1-Compartment Model (Extravascular Administration)
5.1.1 Parameter Estimation of the First-order 1-Compartment Model (Extravascular Administration)
5.1.2 Parameter Estimation of the First-order 1-Compartment Model with Optimal Control
5.1.3 Simulations of the Three First-order 1-Compartment Models
5.1.4 Using Numerical Method to Verify the Explicit Solution of the First-order 1-Compartment SDE Model
5.2 Quantitative Analysis of the First-order 2-Compartment Model (Intravenous Dose)
5.2.1 Parameters Estimation of the First-order 2-Compartment Model(Intravenous Dose)
5.2.2 Parameters Estimation of the First-order 2-Compartment Model with Optimal Control
5.2.3 Simulations of the Three First-order 2-Compartment Models
5.2.4 Stability of the Euler-Maruyama (E-M) Method for the 2-Compartment SDE Model
Appendix
A 1-Compartment ODE Model Simulation
B 1-Compartment Optimal Control Model Simulation
C 1-Compartment SDE Model Simulation
D 2-Compartment ODE Model Simulation
E 2-Compartment Optimal Control Model Simulation
F 2-Compartment SDE Model Simulation
References
刘欠宁,美国新墨西哥州立大学数理统计学博士。现任职于江西财经大学统计学院。教授本科、硕土、博士课程包括贝叶斯统计、随机微分方程、数学分析。
2007年参编教材《线性代数》,中国农业出版社出版。
2018年任SCI期刊International Journal of Biomathematics审稿人。
本专著为本人原创作品。