| 具有时滞的生态-流行病SIS模型的稳定性和Hopf分支 |
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| 引用本文： | 赵红妮,窦霁虹,刘艺艺.具有时滞的生态-流行病SIS模型的稳定性和Hopf分支[J].延安大学学报(自然科学版),2013(2):26-30. |
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| 作者姓名： | 赵红妮 窦霁虹 刘艺艺 |
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| 作者单位： | 西北大学数学系 |
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| 基金项目： | 陕西省教育厅自然科学专项基金(11JK0511) |
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| 摘 要： | 该文考虑一类含有时滞的捕食者染病的生态—流行病SIS模型,主要利用特征根法讨论了平衡点的存在性及其稳定性,证明了当时滞τ=0时,正平衡点是局部渐近稳定的,随着时滞增加,正平衡点由稳定变为不稳定,系统在正平衡点附近产生Hopf分支。
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| 关 键 词： | 生态-流行病模型 渐近稳定 Hopf分支 |
Stability and Hopf Bifurcation of An Eco-Epidemiological SIS Model with Delays |
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| ZHAO Hong-ni,DOU Ji-hong,LIU Yi-yi.Stability and Hopf Bifurcation of An Eco-Epidemiological SIS Model with Delays[J].Journal of Yan'an University(Natural Science Edition),2013(2):26-30. |
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| Authors: | ZHAO Hong-ni DOU Ji-hong LIU Yi-yi |
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| Institution: | (Department of Mathematics,Northwest University,Xi an 710127,China) |
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| Abstract: | A delayed SIS predator- prey epidemiologieal system with disease spreading in predator population is considered. Using the method of characteristic equation the existence and stability of the equilibrium point are ana- lyzed. Positive equilibrium is locally asymptotically stable when time delay T = 0 is showed. While a loss of stability by a Hopf bifurcation can occur as the delays increase. |
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| Keywords: | predator - prey model asymptotically stable Hopf bifurcation |
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