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¡¶ÉúÎïÊýѧ´ÔÊé¡·ÐðPrefaceList 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£º 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¡¶ÉúÎïÊýѧ´ÔÊé¡·Òѳö°æÊéÄ¿