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| 研究生： |
賴維鈞 Wei-Chun Lai |
|---|---|
| 論文名稱： |
The Effect of Cross Infection in a Competition of Two Host for a Single Nutrient via Parasite 交互傳染之數學模型研究 |
| 指導教授： |
許世壁
Sze-Bi Hsu |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 論文出版年： | 2008 |
| 畢業學年度： | 97 |
| 語文別： | 英文 |
| 論文頁數： | 25 |
| 中文關鍵詞： | 資源 、數學模型 、寄生蟲 、競爭 |
| 外文關鍵詞： | resource, mathematical model, parasite, competition |
| 相關次數： | 點閱：2 下載：0 |
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本篇論文主要是延續[1]的工作，探討兩個物種競爭單一資源的模型，而物種本身則被寄生蟲感染而得病。在此我們假設兩物種彼此間會交互感染；在沒有傳染病的時候，物種一的競爭力較物種二為強。我們分析健康與受感染的群體能共存的條件，接著作穩定性的分析。最後我們分析傳染病在兩物種間交互感染的結果，並且與之前的工作結果互相比較。
In [1], we study the mathematical model of two host species competing for a single-limit resource mediated by parasites. Now we assume that there is cross infection between the two host species. We assume that when there is no parasite, species 1 with the smallest break-even concentration, outcompetes species 2. We analyze the model by finding the conditions for the existence of various equilibria, and doing their stability analysis. Finally we compare the results in this paper with those in [1].
[1] Sze-Bi Hsu and I-Fan Sun. Competition of Two Host species for a Single-Limited Resource Mediated by Parasites.
[2] Sze-Bi Hsu. Limiting behavior for competing species. SIAM J. Applied Math. 34, pp. 760-3. (1978)
[3] Sze-Bi Hsu. Ordinary Differential Equation with Applications. World Scientific. (2005)
[4] H. Smith and P. Waltman. The Theory of Chemostat. Cambridge Press. (1994)
[5] P. van den Driessche and James Watmough. Reproduction Numbers and Sub-threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences 180, pp. 29-48. (2002)
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