连续时间和离散时间结构疟疾模型及其动力学分析（英文版）

《生物数学丛书》叙
Preface
List of Symbols
Chapter 1 Introduction
1．1 What is malaria and its public health impact
1．2 The history of malaria
1．2．1 Ancient history of malaria（2700 BC-AD 340）
1．2．2 Discovery of the malaria parasite
1．2．3 Eradication efforts worldwide： success and failure（1955-1978）
1．3 Biology and life cycle of malaria
1．4 The history of mathematical malaria modeling
Chapter 2 Dynamics of continuous-time mosquito population models
2．1 Introduction
2．2 Continuous-time four-stage-structured mosquito population model
2．3 The preliminaries
2．4 The inherent net reproductive number of mosquitoes
2．5 Global dynamics of the continuous-time mosquito population model
2．6 Numerical examples
Chapter 3 Mosquito-stage-structured malaria models and their dynamics
3．1 Introduction
3．2 The model formulation
3．3 Positive invariant sets of the model system
3．4 Infection-free equilibrium and the basic reproductive number Ro
3．5 Endemic equilibria and backward bifurcation
3．6 Global stability of the infection-free equilibrium
3．6．1 Lyapunov function
3．6．2 Global stability of the equilibrium
3．7 Global stability of the endemic equilibrium
3．7．1 Volterra-Goh type Lyapunov function
3．7．2 Global stability of the endemic equilibrium
Chapter 4 Dynamics of discrete-time stage-structured mosquito population models
4．1 Introduction
4．2 The model formulation
4．3 The inherent net reproductive number and dynamics of the trivial equilibrium
4．4 The positive equilibrium
4．4．1 Existence of the positive equilibrium
4．4．2 The stability of the positive equilibrium
4．4．3 Uniform persistence
4．5 Numerical examples
Chapter 5 Simple Discrete-Time Malaria Models
5．1 Population dynamics for mosquitoes and humans without infection
5．2 Discrete-time malaria transmission model
5．3 Constant birth rate and survival rates for mosquitoes
5．3．1 The infection-free equilibrium and the basic reproductiv6 number
5．3．2 Endemic equilibria
5．4 Numerical examples
Chapter 6 Discrete-time mosquito-stage-structured malaria models
6．1 The model formulation
6．2 The infection-free fixed point and the basic reproductive number
Chapter 7 Conclusions
Appendix A Ordinary differential equations
A．1 The initial value problem for ODE systems
A．1．1 Nonautonomous systems
A．1．2 Autonomous systems
A．2 Linear systems of ODE
A．2．1 General linear systems
A．2．2 Linear systems with constant coefficients
A．3 Stability
A．3．1 Stability of linear systems with constant coefficients
A．3．2 Stability by linearization
A．4 Cooperative（quasi-monotone）systems
A．4．1 Cooperative linear systems
A．4．2 Nonlinear autonomous quasi-monotone systems
A．5 Lyapunov methods，LaSalle invariance principle
References
Acknowledgments
Figures
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