血吸虫病动力学模型的稳定性分析
Stability Analysis of Schistosomiasis Dynamic Model
摘要: 血吸虫病是一种严重损害人体器官甚至导致人类死亡的慢性寄生虫病，所以对血吸虫病的干预与控制极为重要。通过研究血吸虫病的传播方式，本文建立了包含毛蚴、尾蚴的单终宿主血吸虫病动力学模型，并计算模型的平衡点与基本再生数。通过Chavez稳定性准则，给出了无病平衡点的全局渐近稳定性，再利用单调动力系统理论得到了地方病平衡点的全局渐近稳定性。为了支持理论研究，最后利用数值模拟对基本再生数进行敏感性分析。
Abstract: Schistosomiasis is a chronic parasitic disease that seriously damages human organs and even leads to human death, so the intervention and control of schistosomiasis are extremely important. By studying the transmission mode of schistosomiasis, a single-terminal host schistosomiasis dynamic model including Trichocariae and cercariae was established, and the equilibrium points and basic reproduction number of the model were calculated. Through Chavez’s stability criterion, the global asymptotic stability of the disease-free equilibrium point is given, and the global asymptotic stability of the endemic equilibrium point is obtained by using monotonic dynamical system theory. In order to support the theoretical research, the sensitivity of the basic regeneration number is analyzed by numerical simulation.
文章引用：杨悦, 黄晓霞, 吕贵臣. 血吸虫病动力学模型的稳定性分析[J]. 理论数学, 2022, 12(12): 2254-2266. https://doi.org/10.12677/PM.2022.1212243

参考文献

[1] George, M. (1965) The Dynamics of Helminth Infections, with Special Reference to Schistosomes. Transactions of the Royal Society of Tropical Medicine & Hygiene, 59, 489-506. [Google Scholar] [CrossRef] [PubMed]
[2] Nasell, I. (1977) On Transmission and Control of Schistosomiasis, with Comments on Macdonald’s Model. Theoretical Population Biology, 12, 335-365. [Google Scholar] [CrossRef] [PubMed]
[3] Barbour, A.D. (1996) Modeling the Transmission of Schistosomiasis: An Introductory View. American Journal of Tropical Medicine and Hygiene, 55, 135-143. [Google Scholar] [CrossRef] [PubMed]
[4] Allen, E.J. and Victory, H.D. (2003) Modelling and Simulation of a Schistosomiasis Infection with Biological Control. Acta Tropica, 87, 251-267. [Google Scholar] [CrossRef] 
[5] 齐龙兴, 薛梦, 甘莉娟, 等. 血吸虫病在两类易感群体中传播的稳定性分析[J]. 安徽大学学报: 自然科学版, 2015, 39(6): 9-14.
[6] Kanyi, E. (2021) Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis. Journal of Applied Mathematics, 2021, Article ID: 6653796. [Google Scholar] [CrossRef] 
[7] Diaby, M. (2015) Stability Analysis of a Schistosomiasis Transmission Model with Control Strategies. BIOMATH, 4, Article ID: 1504161. [Google Scholar] [CrossRef] 
[8] Ronoh, M., Chirove, F., Pedro, S.A., et al. (2021) Modelling the Spread of Schistosomiasis in Humans with Environmental Transmission. Applied Mathematical Modelling, 95, 159-175. [Google Scholar] [CrossRef] 
[9] 罗芬, 向中义. 一类SEIRS流行病模型的研究[J]. 湖北民族学院学报: 自然科学版, 2008, 26(2): 141-145.
[10] Diaby, M., Iggidr, A., Sy, M., et al. (2014) Global Analy-sis of a Schistosomiasis Infection Model with Biological Control. Mathematics and Computation, 246, 731-742. [Google Scholar] [CrossRef] 
[11] Woolhouse, M. (1992) On the Application of Mathematical Models of Schistosome Transmission Dynamics. II. Control. Acta Tropica, 50, 189. [Google Scholar] [CrossRef] 
[12] Hou, Q., Sun, X., Wang, Y., et al. (2014) Global Properties of a General Dynamic Model for Animal Diseases: A Case Study of Brucellosis and Tuberculosis Transmission. Journal of Mathematical Analysis & Applications, 414, 424-433. [Google Scholar] [CrossRef] 
[13] Zou, L. and Ruan, S. (2015) Schistosomiasis Transmission and Control in China. Acta Tropica: Journal of Biomedical Sciences, 143, 51-57. [Google Scholar] [CrossRef] [PubMed]
[14] 金玉娇. 湖北省血吸虫的数学建模和控制[D]: [硕士学位论文]. 武汉: 华中师范大学, 2018.
[15] Li, Y., Teng, Z., Ruan, S., et al. (2017) A Mathematical Model for the Seasonal Transmission of Schistosomiasis in the Lake and Marshland Regions of China. Mathematical Biosciences & Engineering, 14, 1279-1299. [Google Scholar] [CrossRef] [PubMed]
[16] Zhang, T.L. and Zhao, X.-Q. (2010) A Multi-Host Schistosomiasis Model with Seasonality and Time-Dependent Delays. Discrete and Continuous Dynamical Systems B, 50, 5-30.
[17] Wang, W. and Zhao, X. (2008) Threshold Dynamics for Compartmental Epidemic Models in Periodic En-vironments. Journal of Dynamics and Differential Equations, 20, 699-717. [Google Scholar] [CrossRef] 
[18] Kadaleka, S., Abelman, S. and Tchuenche, J.M. (2021) A Hu-man-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding. Acta Biotheoretica, 69, 511-541. [Google Scholar] [CrossRef] 
[19] 吕贵臣, 陆征一. 高维系统稳定性的几何判据[M]. 北京: 科学出版社, 2019.
[20] Diekmann, O., Heesterbeek, J. and Metz, J. (1990) On the Definition and the Computation of the Basic Reproduction Ratio R0 in Models for Infectious Diseases in Heterogeneous Populations. Journal of Mathematical Biology, 28, 365-382. [Google Scholar] [CrossRef] 
[21] Chavez, C.C., Feng, Z. and Huang, W. (2002) On the Computation of and Its Role on Global Stability. In: Castillo-Chavez, C., Blower, S., Driessche, P. van D., Kirschner, D. and Yakubu, A.-A., Eds., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction (Minneapolis, MN, 1999), Vol. 125 of the IMA Volumes in Mathematics and its Applications, Springer, New York, 229-250. [Google Scholar] [CrossRef] 
[22] 马知恩, 周义仓, 等. 传染病动力学的数学建模与研究[M]. 北京: 科学出版社, 2004.
[23] Anguelov, R., Lubuma, J. and Dumont, Y. (2012) Mathematical Modeling of Sterile Insect Technology for Control of Anopheles Mosquito. Computers & Mathematics with Applications: An International Journal, 64, 374-389.

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