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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）
作者：吕军亮 著
出版社：科学出版社
出版时间：2016-06-01
ISBN：9787030482563
定价：¥68.00
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内容简介
20世纪80年代初始，国内对“生物数学”发生兴趣的人越来越多，目前从事生物数学研究、学习生物数学的人数之多已居世界之首。为了加强交流，在“中国生物数学学会”和科学出版社的共同努力下，组织了本套《生物数学丛书》，宗旨是促进数学与生物学的相互渗透，促进数学在生物学中的应用，带动生物数学研究的发展，培养国内生物数学人才。《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）》的读者对象是数学和生物学相关专业高年级大学生、研究生、高校教师和科研工作者。
作者简介
暂缺《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）》作者简介
目录
《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
《生物数学丛书》已出版书目
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
《生物数学丛书》已出版书目
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