具有潜伏效应的H7N9型禽流感模型的动力学分析
Dynamical Behaviors of the H7N9 Avian Influenza with Latent Period
DOI: 10.12677/AAM.2017.68110, PDF, HTML, XML, 下载: 1,868  浏览: 5,082  国家自然科学基金支持
作者: 赵亚飞, 苏 强, 吕贵臣：重庆理工大学，重庆
关键词: SI-SEIR模型；基本再生数；全局稳定性；SI-SEIR Model； Basic Reproductive Number； Global Asymptotic Stability
摘要: 本文研究了具有潜伏期的H7N9禽流感病毒的动力学行为。利用LaSalle不变性原理、Bendixson-Dulac判据以及Li-Muldowney几何方法给出了人–禽系统的全局稳定性。
Abstract: In this paper, we investigate the dynamics of the H7N9 avian influenza with latent period. By ap-plying LaSalle invariance principle, Bendixson-Dulac criterion and Li-Muldowney’s geometric ap-proach, some results for the global asymptotic stability of the human-poultry system are obtained.
文章引用：赵亚飞, 苏强, 吕贵臣. 具有潜伏效应的H7N9型禽流感模型的动力学分析[J]. 应用数学进展, 2017, 6(8): 917-925. https://doi.org/10.12677/AAM.2017.68110

参考文献

[1] 中国疾病预防控制中心. 数据统计: 法定传染报告[EB/OL]. http://www.chinacdc.cn/tjsj_6693/fdcrbbg/, 2017-06-29.
[2] 陈永雪. 基于禽中低致病性的H7N9禽流感模型的动力学性质[J]. 生物数学学报, 2014(4): 627-634.
[3] Jiang, Y. and Chen, Y. (2013) Dynamic Analysis of an Infec-tious Disease between Human and Poultry. Journal of Biomathematics, 4, 003.
[4] 殷其琴, 冯光庭, 张兴安. 两类禽流感模型的动力学分析[J]. 应用数学, 2015, 28(3): 481-489.
[5] 陈娜, 刘云芳, 朱思峰. 两类带有接种的H7N9禽流感模型[J]. 数学的实践与认识, 2016, 46(1): 162-169.
[6] 胡新利, 杨亚莉, 赵惠文, 等. 媒体报道对禽流感(H7N9)传播影响的研究[J]. 西北大学学报自然科学版, 2014, 44(4): 525-528.
[7] 胡新利, 刘艳, 陈瑶, 等. 具有饱和治疗率的H7N9 型禽流感模型的动力学性态分析[J]. 纺织高校基础科学学报, 2016, 29(3): 306-311.
[8] 郭树敏, 李学志. 具有常数输入的H7N9 禽流感动力学模型分析[J]. 信阳师范学院学报: 自然科学版, 2017, 30(1): 13-16.
[9] Iwami, S., Takeuchi, Y. and Liu, X. (2007) Avian-Human Influenza Epidemic Model. Mathematical Biosciences, 207, 1-25.
https://doi.org/10.1016/j.mbs.2006.08.001
[10] Eunok, J., Iwami, S., Takeuchi, Y., et al. (2009) Optimal Control Strategy for Prevention of Avian Influenza Pandemic. Journal of Theoretical Biology, 260, 220-229.
https://doi.org/10.1016/j.jtbi.2009.05.031
[11] Li, M.Y. and Muldowney, J.S. (1996) A Geometric Approach to Global-Stability Problems. SIAM Journal on Mathematical Analysis, 27, 1070-1083.
https://doi.org/10.1137/S0036141094266449
[12] Li, M.Y. and Wang, L. (2002) Global Stability in Some SEIR Epidemic Models, Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory. Springer, New York, 295-311.
https://doi.org/10.1007/978-1-4613-0065-6_17
[13] Chen, Y. and Wen, Y. (2015) Global Dynamic Analysis of a H7N9 Avian-Human Influenza Model in an Outbreak Region. Journal of Theoretical Biology, 367, 180-188.
https://doi.org/10.1016/j.jtbi.2014.12.002
[14] Lu, G. and Lu, Z. (2017) Geometric Approach to Global Asymptotic Stability for the SEIRS Models in Epidemiology. Nonlinear Analysis: Real World Applications, 36, 20-43.
https://doi.org/10.1016/j.nonrwa.2016.12.005
[15] La Salle, J.P. (1976) The Stability of Dynamical Systems. CBMS-NSF Regional Conference Series in Applied Mathematics, 27, 1121-1130.
[16] Li, M.Y. and Muldowney, J.S. (1995) Global Stability for the SEIR Model in Epidemiology. Mathematical Biosciences, 125, 155-164.
https://doi.org/10.1016/0025-5564(95)92756-5
[17] Thieme, H.R. (1992) Convergence Results and a Poinca-ré-Bendixson Trichotomy for Asymptotically Autonomous Differential Equations. Journal of Mathematical Biology, 30, 755-763.
https://doi.org/10.1007/BF00173267
[18] Hutson, V. (1984) A Theorem on Average Liapunov Functions. Monatshefte für Mathematik, 98, 267-275.
https://doi.org/10.1007/BF01540776

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