AAM  >> Vol. 9 No. 2 (February 2020)

    不完全CI下Wolbachia传播的离散竞争模型
    Modeling Wolbachia Propagation underIncomplete Cytoplasmic Incompatibility by Discrete Competition Model

  • 全文下载: PDF(1344KB) HTML   XML   PP.153-165   DOI: 10.12677/AAM.2020.92018  
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作者:  

李艺杰,郭志明:广州大学数学与信息科学学院,广东 广州

关键词:
Wolbachia不完全CI竞争离散模型稳定性Wolbachia Incomplete CI Competition Discrete Model Stability

摘要:

登革热是最严重的蚊媒传染病之一,利用Wolbachia氏菌感染野生蚊子来控制蚊媒传染病是一种有效的策略。本文在不完全CI条件下建立了一个离散竞争模型,研究Wolbachia传播动力学行为。我们通过系统地分析平衡点的存在条件和解的全局渐近性态,给出了Wolbachia成功传播的条件以及CI强度对成功传播的影响,最后利用数值模拟验证了主要结论。

Dengue fever is one of the most serious mosquito-borne infectious diseases. Using Wolbachia in-fection mosquitoes to control those diseases is an effective strategy. In this paper, a discrete com-petition model is established to study the dynamic of Wolbachia propagation under incomplete cytoplasmic incompatibility (CI). We systematically analyze the existing conditions of the equilib-rium and global asymptotic behaviors of solutions to this model, then we give the conditions for successful diffusion and the influence of CI strength on the Wolbachia diffusion. Finally, we verify our findings by numerical simulations.

文章引用:
李艺杰, 郭志明. 不完全CI下Wolbachia传播的离散竞争模型[J]. 应用数学进展, 2020, 9(2): 153-165. https://doi.org/10.12677/AAM.2020.92018

参考文献

[1] Kyle, J.L. and Harris. E. (2008) Global Spread and Persistence of Dengue. Annual Review of Microbiology, 62, 71-92.
https://doi.org/10.1146/annurev.micro.62.081307.163005
[2] Bardina, S.V., Bunduc, P., Tripathi, S., et al. (2017) Enhancement of Zika Virus Pathogenesis by Preexisting Antiflavivirus Immunity. Science, 356, 175-180.
https://doi.org/10.1126/science.aal4365
[3] Yen, J.H. and Barr, A.R. (1971) New Hypothesis of the Cause of Cytoplasmic Incompatibility in Culex pipiens L. Nature, 232, 657-658.
https://doi.org/10.1038/232657a0
[4] Xi, Z.Y., Khoo, C.C., Dobson, S.L., et al. (2005) Wolbachia Establishment and Invasion in an Aedes aegypti Laboratory Population. Science, 310, 326-328.
https://doi.org/10.1126/science.1117607
[5] Yu, J.S. (2018) Modeling Mos-quitoes Population Suppression Based on Delay Differential Equations. SIAM Journal of Applied Mathematics, 78, 3168-3187.
https://doi.org/10.1137/18M1204917
[6] Axford, J.K., Ross, P.A., Yeap, H.L., et al. (2016) Fitness of wAlbB Wolbachia Infection in Aedes aegypti: Parameter Estimates in an Outcrossed Background and Potential for Population Invasion. American Journal of Tropical Medicine and Hygiene, 94, 507-516.
https://doi.org/10.4269/ajtmh.15-0608
[7] Farkas, J.Z. and Hinow, P. (2010) Structured and Unstructured Con-tinuous Models for Wolbachia Infections. Bulletin of Mathematical Biology, 72, 2067-2088.
https://doi.org/10.1007/s11538-010-9528-1
[8] Zheng, B., Tang, M.X. and Yu, J.S. (2014) Modeling Wolbachia Spread in Mosquitoes through Delay Differential Equations. SIAM Journal of Applied Mathematics, 74, 734-770.
https://doi.org/10.1137/13093354X
[9] Hu, L.C., Tang, M.X., Wu, Z.D., et al. (2019) The Threshold Infection Level for Wolbachia Invasion in Random Environments. Journal Differential Equations, 266, 4377-4393.
https://doi.org/10.1016/j.jde.2018.09.035
[10] 邱俊雄, 郭文亮, 郑波. 不完全CI下的Wolbachia动力学行为[J]. 广州大学学报, 2016, 15(6): 34-38.
[11] Leslie, P.H. and Gower, J.C. (1958) The Properties of a Stochastic Model for Two Competing Species. Biometrika, 45, 316-330.
https://doi.org/10.1093/biomet/45.3-4.316
[12] Liu, P.Z. and Elaydi, S.N. (2001) Discrete Competitive and Cooperative Models of Lotka-Volterra Type. Journal of Computational Analysis and Applications, 3, 53-73.
https://doi.org/10.1023/A:1011539901001
[13] Elaydi, S.N. (1999) An Introduction to Difference Equations. 2nd Edition, Springer, New York.
https://doi.org/10.1007/978-1-4757-3110-1
[14] Caswell, H. (2001) Matrix Population Models: Construction, Analysis and Interpretation. 2nd Edition, Sinauer Associates, Inc., Sunderland, MA.