| 中文摘要 | 第3-5页 |
| Abstract | 第5-7页 |
| Chapter 1 Introduction | 第10-30页 |
| 1.1 West Nile virus and its transmission | 第10-14页 |
| 1.2 Mathematical models of WNv | 第14-18页 |
| 1.3 Simplified models of WNv | 第18-24页 |
| 1.4 Motivations and contributions | 第24-30页 |
| Chapter 2 Spreading and vanishing in a WNv model with expandingfronts | 第30-64页 |
| 2.1 The model with expanding fronts | 第30-33页 |
| 2.2 Existence and uniqueness of the solution | 第33-40页 |
| 2.3 The risk index of WNv | 第40-42页 |
| 2.4 The vanishing of WNv | 第42-50页 |
| 2.5 The spreading of WNv | 第50-60页 |
| 2.6 Numerical simulations and discussions | 第60-64页 |
| Chapter 3 Coexistence of a cross-diffusive WNv model in a hetero-geneous environment | 第64-84页 |
| 3.1 The WNv model with cross-diffusion | 第64-68页 |
| 3.2 Basic reproduction numbers | 第68-72页 |
| 3.3 Existence of coexistence | 第72-77页 |
| 3.4 Non-existence of coexistence | 第77-79页 |
| 3.5 Iteration and true solution | 第79-82页 |
| 3.6 Numerical simulations and discussions | 第82-84页 |
| Chapter 4 Asymptotic periodicity in a diffusive WNv model in aheterogeneous environment | 第84-102页 |
| 4.1 Periodic phenomena and the model | 第84-86页 |
| 4.2 Basic reproduction numbers | 第86-90页 |
| 4.3 Existence and non-existence of periodic solution | 第90-93页 |
| 4.4 The maximal and minimal periodic solutions | 第93-95页 |
| 4.5 Attractivity of periodic solutions | 第95-98页 |
| 4.6 Numerical simulations and discussions | 第98-102页 |
| Chapter 5 The spatial-temporal risk index and transmission dynam-ics for a time-periodic diffusive WNv model | 第102-134页 |
| 5.1 Periodic surrounding and free boundary | 第102-106页 |
| 5.2 Preliminaries | 第106-108页 |
| 5.3 The spatial-temporal risk index | 第108-113页 |
| 5.4 The T-periodic boundary value problem in half line | 第113-120页 |
| 5.5 Spreading and vanishing | 第120-130页 |
| 5.6 Numerical simulations and discussions | 第130-134页 |
| Chapter 6 Conclusions and future research | 第134-138页 |
| Bibliography | 第138-152页 |
| Publications | 第152-154页 |
| Acknowledgements | 第154-156页 |
