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| 摘要: |
| 本文研究了一类三维生态传染病模型的正解性和边界性,并分析了系统平衡点的局部稳定性.利用一种新的几何方法,获得了内平衡点的全稳定性,推广了Li和Muldowney[1]提出的这种方法的应用,这种方法避免了寻找Lyapunov的困难. |
| 关键词: 捕食者与被捕食者 疾病 Hopf分支 全局稳定 |
| DOI： |
| 分类号:O175.13 |
| 基金项目:Supported by National Natural Science Foundation of China (10671182). |
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| GLOBAL STABILITY FOR A PREDATOR-PREY MODEL WITH DISEASE IN THE PREY |
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LIU Xi-xian,LI Bi-wen,CHEN Bo-shan
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| Abstract: |
| This paper describes a three dimensional eco-epidemiological model consisting of susceptible prey, infected prey and predator. We consider the positivity and boundedness of the solution first and the local stability of the equilibrium is discussed. Obviously, the interior equilibrium A* is always locally asymptotically stable according to the Routh-Hurwitz criterion. At last, the geometric method of Li and Muldowney is used to investigate the global stability of the interior equilibrium. |
| Key words: predator-prey disease geometric method global stability |
