具有垂直传染和分布时滞的SEI传染病模型
SEI Infectious Disease Model with Vertical Transmission and Distribution Time Delay
DOI: 10.12677/AAM.2022.1111794, PDF,    科研立项经费支持
作者: 卢 旸, 王倩兰, 徐钰滢：东北石油大学数学与统计学院应用数学系，黑龙江 大庆
关键词: SEI传染病模型；分布时滞；垂直传染；全局稳定性；持久性；SEI Infectious Disease Model； Distribution Time Delay； Vertical Transmission； Global Stability； Persistence
摘要: 本文以北美僵尸鹿传染病传播特征为生物背景，建立了具有垂直传染和分布时滞的SEI传染病模型。通过定义界定疾病是否传播的基本再生数R0，分别给出了模型无病平衡点全局渐近稳定以及患病鹿群持久生存的充分条件：即当R0 ≤ 1时，无病平衡点E0是全局渐近稳定的；当R0 > 1时，患病鹿群是持久的。文末的数值模拟不仅验证了定性理论结果的正确性，同时展示了僵尸鹿病毒潜伏期和死亡率对鹿种群数量的影响。
Abstract: In this paper, we study an SEI infectious disease model with vertical transmission and distribution time delay that was developed using the infectious disease transmission characteristics of zombie deer in North America as the biological background. By defining the basic reproduction number that defines whether the disease is transmitted or not, sufficient conditions are given for the global asymptotic stability of the disease-free equilibrium point and the persistence of the diseased deer population, respectively: when the basic reproduction number less than or equal to one, the dis-ease-free equilibrium point is globally asymptotically stable; when the basic reproduction number greater than one, the diseased deer population is persistent. The numerical simulation at the end of the paper not only verifies the correctness of the qualitative theoretical results, but also demon-strates the effects of zombie deer virus incubation period and mortality on deer population size.
文章引用：卢旸, 王倩兰, 徐钰滢. 具有垂直传染和分布时滞的SEI传染病模型[J]. 应用数学进展, 2022, 11(11): 7493-7502. https://doi.org/10.12677/AAM.2022.1111794

参考文献

[1] Ruan, S.G. and Wang, W.D. (2003) Dynamical Behavior of an Epidemic Model with a Nonlinear Incidence Rate. Jour-nal of Differential Equations, 188, 135-163. [Google Scholar] [CrossRef] 
[2] Li, M.Y., Smith, H.L. and Wang, L.C. (2001) Global Dynamics of an SEIR Epidemic Model with Vertical Transmission. SIAM Journal on Applied Mathematics, 62, 58-69. [Google Scholar] [CrossRef] 
[3] Meng, X.Z., Chen, L.S. and Cheng, H.D. (2007) Two Profitless Delays for the SEIRS Epidemic Disease Model with Nonlinear Incidence and Pulse Vaccination. Applied Mathematics and Computation, 186, 516-529. [Google Scholar] [CrossRef] 
[4] Li, D., Liu, S.Q. and Cui, J.A. (2017) Threshold Dynamics and Ergodicity of an SIRS Epidemic Model with Markovian Switching. Journal of Differential Equations, 263, 8873-8915. [Google Scholar] [CrossRef] 
[5] Chen, X. and Cui, R. (2020) Global Stability in a Diffusive Cholera Epidemic Model with Nonlinear Incidence. Applied Mathematics Letters, 111, Article ID: 106596. [Google Scholar] [CrossRef] 
[6] Zhang, J., Li, J.Q. and Ma, Z.E. (2004) Global Analysis of SIR Epidemic Models with Population Size Dependent Contact Rate. Chinese Journal of Engineering Mathematics, 21, 259-267.
[7] Jiao, J., Liu, Z. and Cai, S. (2020) Dynamics of an SEIR Model with Infectivity in Incubation Period and Homestead-Isolation on the Susceptible. Applied Mathematics Letters, 107, Article ID: 106442. [Google Scholar] [CrossRef] [PubMed]
[8] 傅金波, 陈兰荪. 具有垂直传染和接触传染的传染病模型的稳定性研究[J]. 数学杂志, 2016, 36(6): 1283-1290.
[9] Liu, Q., Jiang, D.Q. and Shi, N.Z. (2017) Stationarity and Pe-riodicity of Positive Solutions to Stochastic SEIR Epidemic Models with Distributed Delay. Discrete and Continuous Dynamical Systems—Series B, 22, 2479-2500. [Google Scholar] [CrossRef] 
[10] Zhang, T. and Teng, Z. (2009) Permanence and Extinction for a Non-Autonomous SIRS Epidemic Model with Time Delay. Applied Mathematical Modelling, 33, 1058-1071. [Google Scholar] [CrossRef] 
[11] Collinge, J. (2001) Prion Diseases of Humans and Animals: Their Causes and Molecular Basis. Annual Review of Neuroscience, 24, 519-550. [Google Scholar] [CrossRef] [PubMed]
[12] O’Rourke, K.I., Besser, T.E. and Miller, M.W. (1999) PrP Genotypes of Captive and Free-Ranging Rocky Mountain Elk (Cervus elaphus nelsoni) with Chronic Wasting Disease. Journal of General Virology, 80, 2765-2769. [Google Scholar] [CrossRef] [PubMed]
[13] Johnson, C. (2006) Prion Protein Polymorphisms in White-Tailed Deer Influence Susceptibility to Chronic Wasting Disease. Journal of General Virology, 87, 2109-2114. [Google Scholar] [CrossRef] [PubMed]
[14] Mammadova, N., Cassmann, E. and Greenlee, J.J. (2020) Successful Transmission of the Chronic Wasting Disease (CWD) Agent to White-Tailed Deer by Intravenous Blood Transfusion. Research in Veterinary Science, 133, 304-306. [Google Scholar] [CrossRef] [PubMed]
[15] 张伯强, 张体银, 姚光国. 鹿慢性消耗性疾病研究进展[J]. 中国动物检疫, 2009, 26(8): 69-72.
[16] 王晶, 石琦. 慢性消耗性疾病的实验室生物安全评价[J]. 病毒学报, 2018, 34(3): 402-405.
[17] Rivera, N.A., Brandt, A.L., Novakofski, J.E., et al. (2019) Chronic Wasting Disease in Cervids: Prevalence, Impact and Management Strategies. Veterinary Medicine: Research and Reports, 10, 123-139. [Google Scholar] [CrossRef] 
[18] Tranulis, M.A., Tryland, M., Kapperud, G., et al. (2019) CWD in Norway. European Journal of Nutrition and Food Safety, 9, 301-302. [Google Scholar] [CrossRef] 
[19] 李冬梅, 卢旸, 刘伟华. 一类具有连续接种的自治SEIR传染病模型[J]. 哈尔滨理工大学学报, 2013, 18(1): 67-72.
[20] 徐为坚. 具有免疫接种及饱和传染率的传染病模型分析[J]. 玉林师范学院学报, 2007, 28(5): 261-263.
[21] 马知恩, 周义仓. 常微分方程定性与稳定性方法[M]. 北京: 科学出版社, 2001.

为你推荐