Search Advanced

Mathematical Biosciences and Engineering

2007, Volume 4, Issue 4: 567-572. doi: 10.3934/mbe.2007.4.567
Previous Article Next Article

Global stability of equilibria in a tick-borne disease model

  • 1.
    Department of Mathematical Sciences, University of Alabama in Huntsville, Huntsville, AL 35899
  • 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] Robert Carlson . Myopic models of population dynamics on infinite networks. Networks and Heterogeneous Media, 2014, 9(3): 477-499. doi: 10.3934/nhm.2014.9.477
    [2] Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco . A simple and bounded model of population dynamics for mutualistic networks. Networks and Heterogeneous Media, 2015, 10(1): 53-70. doi: 10.3934/nhm.2015.10.53
    [3] Riccardo Bonetto, Hildeberto Jardón Kojakhmetov . Nonlinear diffusion on networks: Perturbations and consensus dynamics. Networks and Heterogeneous Media, 2024, 19(3): 1344-1380. doi: 10.3934/nhm.2024058
    [4] Claudio Canuto, Anna Cattani . The derivation of continuum limits of neuronal networks with gap-junction couplings. Networks and Heterogeneous Media, 2014, 9(1): 111-133. doi: 10.3934/nhm.2014.9.111
    [5] Elisabeth Logak, Isabelle Passat . An epidemic model with nonlocal diffusion on networks. Networks and Heterogeneous Media, 2016, 11(4): 693-719. doi: 10.3934/nhm.2016014
    [6] Narcisa Apreutesei, Vitaly Volpert . Reaction-diffusion waves with nonlinear boundary conditions. Networks and Heterogeneous Media, 2013, 8(1): 23-35. doi: 10.3934/nhm.2013.8.23
    [7] Juan Manuel Pastor, Javier García-Algarra, José M. Iriondo, José J. Ramasco, Javier Galeano . Dragging in mutualistic networks. Networks and Heterogeneous Media, 2015, 10(1): 37-52. doi: 10.3934/nhm.2015.10.37
    [8] Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond . A new model for the emergence of blood capillary networks. Networks and Heterogeneous Media, 2021, 16(1): 91-138. doi: 10.3934/nhm.2021001
    [9] Mirela Domijan, Markus Kirkilionis . Graph theory and qualitative analysis of reaction networks. Networks and Heterogeneous Media, 2008, 3(2): 295-322. doi: 10.3934/nhm.2008.3.295
    [10] Luca Di Persio, Giacomo Ziglio . Gaussian estimates on networks with applications to optimal control. Networks and Heterogeneous Media, 2011, 6(2): 279-296. doi: 10.3934/nhm.2011.6.279
  • 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. Zlatinka Dimitrova, Flows of Substances in Networks and Network Channels: Selected Results and Applications, 2022, 24, 1099-4300, 1485, 10.3390/e24101485
    2. Agelos Georgakopoulos, Sebastian Haeseler, Matthias Keller, Daniel Lenz, Radosław K. Wojciechowski, Graphs of finite measure, 2015, 103, 00217824, 1093, 10.1016/j.matpur.2014.10.006
  • 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
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(2365) PDF downloads(478) Cited by(6)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog