Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection

  • Received: 01 August 2012 Accepted: 29 June 2018 Published: 01 August 2013
  • MSC : Primary: 37N25, 37G10; Secondary: 92B05.

  • A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied.The condition for the global stability of the disease free equilibrium is obtained.The existence of the endemic equilibrium and its stability are investigated.More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation.Sufficient conditions for those bifurcations have been obtained.Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

    Citation: Hui Cao, Yicang Zhou, Zhien Ma. Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1399-1417. doi: 10.3934/mbe.2013.10.1399

    Related Papers:

  • A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied.The condition for the global stability of the disease free equilibrium is obtained.The existence of the endemic equilibrium and its stability are investigated.More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation.Sufficient conditions for those bifurcations have been obtained.Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.


    加载中
    [1] Math. Biosci., 124 (1994), 83-105.
    [2] Math. Biosci., 163 (2000), 1-33.
    [3] J. Differ. Equ. Appl., 14 (2008), 1127-1147.
    [4] Available from: http://mtbi.asu.edu/files/Discrete_time_SEIS_Models_with_Exogenous_Reinfection_and_Dispersal_between_Two_Patches.pdf.
    [5] Numer. Funct. Anal. Optimiz., 9 (1987), 381-414.
    [6] Math. Model. Appl., 1 (2012), 33-37.
    [7] INT. J. Bio., 5 (2012), 61-76.
    [8] Math. Comput. Model., 55 (2012), 385-395.
    [9] Discrete Cont. Dyn. Sys. B, 18 (2013), 37-56.
    [10] Discrete Dyn. Nat. Soc., (2011), Art. ID 653937, 21 pp.
    [11] Nonliear Anal. TMA, 47 (2001), 4753-4762.
    [12] in "Mathematical Approaches for Emerging and Reemerging Infectious Diseases: A introduction" (eds. C. Castillo-Chavez with S. Blower, P. van den Driessche, D. Kirschner and A. A. Yakubu), Springer-Verlag, New York, (2002), 153-163.
    [13] Chaos Soliton. Fract., 40 (2009), 1956-1962.
    [14] SIAM J. Appl. Math., 66 (2006), 1563-1587.
    [15] MTBI technical Report, 2000.
    [16] Research in Economics, 62 (2008), 120-177.
    [17] Springer, New York, 1983.
    [18] J. Anim. Ecol., 44 (1975), 283-289.
    [19] Nonlinear Anal. RWA, 13 (2012), 2017-2033.
    [20] Nonlinear Anal. RWA, 12 (2011), 2356-2377.
    [21] Appl. Math. Comput., 216 (2010), 1226-1234.
    [22] Chaos Solution. Fract., 26 (2005), 947-958.
    [23] J. Theor. Biol., 51 (1975), 511-524.
    [24] Nature, 256 (1975), 165-166.
    [25] Nature, 261 (1976), 459-467.
    [26] J. Math. Biol., 30 (1992), 755-763.
    [27] Comm. Appl. Nonl. Anal., 3 (1996), 43-66.
    [28] in "A Survey of Mathematical Biology, Fields Communications Series" (ed. S. Sivaloganathan), 57, A co-publication of the AMS and Fields Institute, Canada, (2010), 83-112.
    [29] J. Theor. Biol., 254 (2008), 215-228.
    [30] Math. Biosci. Eng., 6 (2009), 409-425.
    [31] Math. Comput. Model., 40 (2004), 1491-1506.
    [32] Discrete Cont. Dyn. Sys. B, 4 (2004), 843-852.
  • Reader Comments
  • © 2013 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(1600) PDF downloads(544) Cited by(9)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog