连续时间和离散时间结构疟疾模型及其动力学分析-18

《生物数学丛书》叙PrefaceList of SymbolsChapter 1 Introduction1．1 What is malaria and its public health impact1．2 The history of malaria1．2．1 Ancient history of malaria（2700 BC-AD 340）1．2．2 Discovery of the malaria parasite1．2．3 Eradication efforts worldwide： success and failure（1955-1978）1．3 Biology and life cycle of malaria1．4 The history of mathematical malaria modeling Chapter 2 Dynamics of continuous-time mosquito population models2．1 Introduction2．2 Continuous-time four-stage-structured mosquito population model2．3 The preliminaries2．4 The inherent net reproductive number of mosquitoes2．5 Global dynamics of the continuous-time mosquito population model2．6 Numerical examplesChapter 3 Mosquito-stage-structured malaria models and their dynamics3．1 Introduction3．2 The model formulation3．3 Positive invariant sets of the model system3．4 Infection-free equilibrium and the basic reproductive number Ro3．5 Endemic equilibria and backward bifurcation3．6 Global stability of the infection-free equilibrium3．6．1 Lyapunov function3．6．2 Global stability of the equilibrium3．7 Global stability of the endemic equilibrium3．7．1 Volterra-Goh type Lyapunov function3．7．2 Global stability of the endemic equilibriumChapter 4 Dynamics of discrete-time stage-structured mosquito population models4．1 Introduction4．2 The model formulation4．3 The inherent net reproductive number and dynamics of the trivial equilibrium4．4 The positive equilibrium4．4．1 Existence of the positive equilibrium4．4．2 The stability of the positive equilibrium4．4．3 Uniform persistence4．5 Numerical examplesChapter 5 Simple Discrete-Time Malaria Models5．1 Population dynamics for mosquitoes and humans without infection5．2 Discrete-time malaria transmission model5．3 Constant birth rate and survival rates for mosquitoes5．3．1 The infection-free equilibrium and the basic reproductiv6 number\"5．3．2 Endemic equilibria5．4 Numerical examplesChapter 6 Discrete-time mosquito-stage-structured malaria models6．1 The model formulation6．2 The infection-free fixed point and the basic reproductive number Chapter 7 ConclusionsAppendix A Ordinary differential equationsA．1 The initial value problem for ODE systemsA．1．1 Nonautonomous systemsA．1．2 Autonomous systemsA．2 Linear systems of ODEA．2．1 General linear systemsA．2．2 Linear systems with constant coefficientsA．3 StabilityA．3．1 Stability of linear systems with constant coefficientsA．3．2 Stability by linearizationA．4 Cooperative（quasi-monotone）systemsA．4．1 Cooperative linear systemsA．4．2 Nonlinear autonomous quasi-monotone systemsA．5 Lyapunov methods，LaSalle invariance principleReferencesAcknowledgmentsFigures《生物数学丛书》已出版书目