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

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  • 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.
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    [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.

    © 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)
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