Threshold Conditions for West Nile Virus Outbreaks
Threshold Conditions for West Nile Virus Outbreaks
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西尼罗河病毒爆发的阈值条件
DOI：
10.1007/s11538-008-9374-6
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发表时间：
2009-04-01
影响因子：
3.5
通讯作者：
Zhu, Huaiping
中科院分区：
文献类型：
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作者：
Jiang, Jifa;Qiu, Zhipeng;Zhu, Huaiping
在本文中，我们研究了西尼罗河病毒传播动力学模型的稳定性和鞍结分支。给出了平衡点的存在性和分类。利用K-竞争动力系统理论和曲面上动力系统的指标理论，得到了平衡点局部稳定的充要条件。我们还研究了系统的鞍结分岔。在参数方面的显式亚阈值条件下获得超出基本繁殖数，这为访问控制西尼罗河病毒的传播提供了进一步的指导方针。我们的研究结果表明，基本繁殖数本身并不足以描述西尼罗河病毒是否会流行，并建议我们应该更多地关注西尼罗河病毒的初始状态。这一结果也部分解释了该病毒在北美小规模流行的复发机制。
In this paper, we study the stability and saddle-node bifurcation of a model for the West Nile virus transmission dynamics. The existence and classification of the equilibria are presented. By the theory of K-competitive dynamical systems and index theory of dynamical systems on a surface, sufficient and necessary conditions for local stability of equilibria are obtained. We also study the saddle-node bifurcation of the system. Explicit subthreshold conditions in terms of parameters are obtained beyond the basic reproduction number which provides further guidelines for accessing control of the spread of the West Nile virus. Our results suggest that the basic reproductive number itself is not enough to describe whether West Nile virus will prevail or not and suggest that we should pay more attention to the initial state of West Nile virus. The results also partially explained the mechanism of the recurrence of the small scale endemic of the virus in North America.