| 疾病在食饵中流行的捕食与被捕食模型的分析 |
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| 引用本文： | 康爱花,薛亚奎.疾病在食饵中流行的捕食与被捕食模型的分析[J].数学的实践与认识,2007,37(20):77-81. |
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| 作者姓名： | 康爱花 薛亚奎 |
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| 作者单位： | 中北大学,数学系,山西,太原,030051 |
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| 基金项目： | 国家自然科学基金;山西省自然科学基金;山西省教育厅资助项目 |
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| 摘 要： | 分析并建立了疾病在食饵中传播的生态-传染病模型,同时考虑到两种群都受密度制约因素的影响,讨论了模型解的有界性和各平衡点的存在性,利用Routh-Hurwitz判据证明了各平衡点的局部渐进稳定性,通过构造Lyapunov函数分析了各平衡点的全局渐进稳定性,得到了疾病存在与否的充分性条件.
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| 关 键 词： | 生态-传染病模型 渐进稳定 全局稳定 |
| 修稿时间： | 2007年4月3日 |
The Dynamic of the Eco-epidemiological Model with the Disease in the Prey |
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| KANG Ai-hua,XUE Ya-kui.The Dynamic of the Eco-epidemiological Model with the Disease in the Prey[J].Mathematics in Practice and Theory,2007,37(20):77-81. |
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| Authors: | KANG Ai-hua XUE Ya-kui |
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| Abstract: | We analyze and formulate the eco-epidemiological model with the disease in the prey,considering density-dependent of two species.The boundness of solutions and the existence of the equilibria are studied,and the sufficient conditions of locally asymptotically stable of the equilibria are obtained by the Routh-Hurwitz criterion.Furthermore,we analyze the global stability of the equilibria by using Lyapunov functions,and obtain the conditions of the disease extincting and the disease persistence. |
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| Keywords: | eco-epidemiological model asymptotically stability global stability |
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