Table of Contents

1. Title Page and Abstract
2. Chapter 1: Introduction and Background
3. Chapter 2: A Bifurcation Theorem for Resident-Invader Type Population
   1. 2.1 Introduction
   2. 2.2 Bifurcation Analysis of a Resident-Invader System of Host-Parasitoid Type
   3. 2.3 An SIR Model with Demographic Population Cycles
      1. 2.3.1 Numerical Examples
   4. 2.4 Concluding Remarks
4. Chapter 3: A Discrete-Time Stage-Structured Host-Parasitoid Model
   1. 3.1 Introduction
   2. 3.2 The Host-Parasitoid Model
   3. 3.3 Dynamics of the Model
      1. 3.3.1 Boundary Dynamics
      2. 3.3.2 Interior Dynamics
   4. 3.4 The Impact of Continuous Pesticide Spraying
   5. 3.5 Concluding Remarks
5. Chapter 4: Host-Parasitoid Model with Periodic Impulsive Effects
   1. 4.1 Introduction
   2. 4.2 The Impulsive Host-Parasitoid Model
   3. 4.3 Existence and Global Stability of Host-Eradication Periodic Solutions
   4. 4.4 Numerical Study of the Impulsive Model
   5. 4.5 Concluding Remarks
6. Chapter 5: A Discrete-Time SIS Model with Vaccination
   1. 5.1 Introduction
   2. 5.2 Model Formulation
   3. 5.3 Model Analysis
      1. 5.3.1 R₀ and the Disease-Free Equilibrium
      2. 5.3.2 Endemic Dynamics
   4. 5.4 An Alternative Model Formulation
   5. 5.5 Impact of Vaccination on the Backward Bifurcation
   6. 5.6 Concluding Remarks
7. Chapter 6: Conclusion and Future Work
   1. 6.1 Summary and Future Works for Chapter 3
   2. 6.2 Summary and Future Works for Chapter 4
   3. 6.3 Summary and Future Works for Chapter 5
8. Bibliography
9. Appendix
10. Biographical Sketch