Global stability of equilibria in a tick-borne disease model

  • Received: 01 April 2007 Accepted: 29 June 2018 Published: 01 August 2007
  • MSC : 34C60, 34D23, 92D30.

  • In this short note we establish global stability results for a four-dimensional nonlinear system that was developed in modeling a tick-borne disease by H.D. Gaff and L.J. Gross (Bull. Math. Biol., 69 (2007), 265--288) where local stability results were obtained. These results provide the parameter ranges for controlling long-term population and disease dynamics.

    Citation: Shangbing Ai. Global stability of equilibria in a tick-borne disease model[J]. Mathematical Biosciences and Engineering, 2007, 4(4): 567-572. doi: 10.3934/mbe.2007.4.567

    Related Papers:

    [1] Ardak Kashkynbayev, Daiana Koptleuova . Global dynamics of tick-borne diseases. Mathematical Biosciences and Engineering, 2020, 17(4): 4064-4079. doi: 10.3934/mbe.2020225
    [2] Holly Gaff, Robyn Nadolny . Identifying requirements for the invasion of a tick species and tick-borne pathogen through TICKSIM. Mathematical Biosciences and Engineering, 2013, 10(3): 625-635. doi: 10.3934/mbe.2013.10.625
    [3] Holly Gaff . Preliminary analysis of an agent-based model for a tick-borne disease. Mathematical Biosciences and Engineering, 2011, 8(2): 463-473. doi: 10.3934/mbe.2011.8.463
    [4] Marco Tosato, Xue Zhang, Jianhong Wu . A patchy model for tick population dynamics with patch-specific developmental delays. Mathematical Biosciences and Engineering, 2022, 19(5): 5329-5360. doi: 10.3934/mbe.2022250
    [5] Maeve L. McCarthy, Dorothy I. Wallace . Optimal control of a tick population with a view to control of Rocky Mountain Spotted Fever. Mathematical Biosciences and Engineering, 2023, 20(10): 18916-18938. doi: 10.3934/mbe.2023837
    [6] Yijun Lou, Li Liu, Daozhou Gao . Modeling co-infection of Ixodes tick-borne pathogens. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1301-1316. doi: 10.3934/mbe.2017067
    [7] Ning Yu, Xue Zhang . Discrete stage-structured tick population dynamical system with diapause and control. Mathematical Biosciences and Engineering, 2022, 19(12): 12981-13006. doi: 10.3934/mbe.2022606
    [8] Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva . Global dynamics of a vector-host epidemic model with age of infection. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1159-1186. doi: 10.3934/mbe.2017060
    [9] Fahad Al Basir, Yasuhiro Takeuchi, Santanu Ray . Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission. Mathematical Biosciences and Engineering, 2021, 18(1): 583-599. doi: 10.3934/mbe.2021032
    [10] Rundong Zhao, Qiming Liu, Huazong Zhang . Dynamical behaviors of a vector-borne diseases model with two time delays on bipartite networks. Mathematical Biosciences and Engineering, 2021, 18(4): 3073-3091. doi: 10.3934/mbe.2021154
  • In this short note we establish global stability results for a four-dimensional nonlinear system that was developed in modeling a tick-borne disease by H.D. Gaff and L.J. Gross (Bull. Math. Biol., 69 (2007), 265--288) where local stability results were obtained. These results provide the parameter ranges for controlling long-term population and disease dynamics.


  • This article has been cited by:

    1. A.K. Misra, Vishal Singh, A delay mathematical model for the spread and control of water borne diseases, 2012, 301, 00225193, 49, 10.1016/j.jtbi.2012.02.006
    2. A.K. Misra, S.N. Mishra, A.L. Pathak, P.K. Srivastava, Peeyush Chandra, A mathematical model for the control of carrier-dependent infectious diseases with direct transmission and time delay, 2013, 57, 09600779, 41, 10.1016/j.chaos.2013.08.002
    3. Jane M. Heffernan, Yijun Lou, Jianhong Wu, Range expansion of Ixodes scapularis ticks and of Borrelia burgdorferi by migratory birds, 2014, 19, 1553-524X, 3147, 10.3934/dcdsb.2014.19.3147
    4. Naret Ruttanaprommarin, Zulqurnain Sabir, Rafaél Artidoro Sandoval Núñez, Soheil Salahshour, Juan Luis García Guirao, Wajaree Weera, Thongchai Botmart, Anucha Klamnoi, Artificial neural network procedures for the waterborne spread and control of diseases, 2022, 8, 2473-6988, 2435, 10.3934/math.2023126
    5. Kalyan Kumar Pal, Rajanish Kumar Rai, Pankaj Kumar Tiwari, Impact of psychological fear and media on infectious diseases induced by carriers, 2024, 34, 1054-1500, 10.1063/5.0217936
    6. Shikha Singh, Shubham Chaudhry, Maninder Singh Arora, Rajeev Kumar Singh, Arvind Kumar Misra, Modeling the effect of temperature rise due to atmospheric carbon dioxide on the outbreak of food-borne diseases, 2025, 1598-5865, 10.1007/s12190-024-02336-5
  • Reader Comments
  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2399) PDF downloads(478) Cited by(6)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog