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Mathematical Biosciences and Engineering

2015, Volume 12, Issue 3: 473-490. doi: 10.3934/mbe.2015.12.473
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The effect of time delay in plant--pathogen interactions with host demography

  • 1.
    Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples
  • 2.
    Department of Mathematics, University of Portsmouth, Portsmouth, PO1 3HF
  • Received: 01 April 2014 Accepted: 29 June 2018 Published: 01 January 2015

  • MSC : Primary: 92D30; Secondary: 34K20, 37N25.

  • Botanical epidemic models are very important tools to study invasion, persistence and control of diseases. It is well known that limitations arise from considering constant infection rates. We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. Sufficient conditions for the global stability of the pathogen-free equilibrium and the permanence of the system are among the results obtained through qualitative analysis. We also show that the delay can cause stability switches of the coexistence equilibrium. In the undelayed case, we prove that the onset of oscillations may occur through Hopf bifurcation.

    Citation: Bruno Buonomo, Marianna Cerasuolo. The effect of time delay in plant--pathogen interactions with host demography[J]. Mathematical Biosciences and Engineering, 2015, 12(3): 473-490. doi: 10.3934/mbe.2015.12.473

    Related Papers:

  • Botanical epidemic models are very important tools to study invasion, persistence and control of diseases. It is well known that limitations arise from considering constant infection rates. We replace this hypothesis in the framework of delay differential equations by proposing a delayed epidemic model for plant--pathogen interactions with host demography. Sufficient conditions for the global stability of the pathogen-free equilibrium and the permanence of the system are among the results obtained through qualitative analysis. We also show that the delay can cause stability switches of the coexistence equilibrium. In the undelayed case, we prove that the onset of oscillations may occur through Hopf bifurcation.


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    [1] Nature, 280 (1979), 361-367.
    [2] Oxford University Press, Oxford and New York, 1991.
    [3] Math. Biosci. Eng., 8 (2011), 931-952.
    [4] SIAM J. Math. Anal., 33 (2002), 1144-1165.
    [5] J. Math. Biol., 33 (1995), 250-260.
    [6] John Wiley and Sons, Boston, 1982.
    [7] Appl. Math. Comput., 232 (2014), 858-871.
    [8] Springer, Berlin, 1993.
    [9] Math. Biosci. Engin., 1 (2004), 361-404.
    [10] J. Royal Soc. Interface, 7 (2010), 439-451.
    [11] J. Theor. Biol., 278 (2011), 32-43.
    [12] Phytopathology, 102 (2012), 365-380.
    [13] J. Math. Biol., 36 (1998), 227-248.
    [14] Adv. Bot. Res., 38 (2002), 1-64.
    [15] Philos. T. Roy. Soc. B, 363 (2008), 741-759.
    [16] Annu. Rev. Phytopathol., 46 (2008), 385-418.
    [17] Theor. Pop. Biol., 57 (2000), 219-233.
    [18] Springer-Verlag, Berlin, 1983.
    [19] SIAM J. Math. Anal., 20 (1989), 388-395.
    [20] J. Math. Biol., 63 (2011), 125-139.
    [21] Plant Pathol., 35 (1986), 355-361.
    [22] Physiol. Entomol., 29 (2004), 291-304.
    [23] J. Theor. Biol., 256 (2009), 201-214.
    [24] Phytopathology, 84 (1994), 24-27.
    [25] Virus Res., 159 (2011), 215-222.
    [26] Math. Med. Biol., 15 (1998), 1-18.
    [27] Math. Biosci. Eng., 3 (2006), 101-109.
    [28] Academic Press, 1993.
    [29] Math. Biosci., 160 (1999), 191-213.
    [30] J. Math. Anal. Appl., 182 (1994), 250-256.
    [31] Appl. Math. Lett., 17 (2004), 1141-1145.
    [32] Tohoku Math. J., 54 (2002), 581-591.
    [33] Eur. J. Plant Path., 115 (2006), 3-23.
    [34] American Phytopathological Society, St Paul, MN, 2007.
    [35] Nature, 280 (1979), 455-461.
    [36] Nonlinear Anal. RWA, 11 (2010), 55-59.
    [37] Plant Disease, 85 (2001), 1122-1122.
    [38] SIAM J. Appl. Math., 62 (2001), 58-69.
    [39] John Wiley & Sons, 2006.
    [40] Nonlinear Anal., 42 (2000), 931-947.
    [41] Dynamical Systems, 27 (2012), 145-160.
    [42] Math. Methods Appl. Sci., 30 (2007), 733-749.
    [43] J. Appl. Ecol., 43 (2006), 506-516.
    [44] Proc. Royal Soc. Lond. B Biol., 274 (2007), 11-18.
    [45] Phytopathology, 98 (2008), 239-249
    [46] Math. Biosci., 180 (2002), 29-48.
    [47] Academic Press, 1963.
    [48] J. Appl. Math. Comput., 35 (2011), 229-250.
    [49] Nonlinear Dynam., 61 (2010), 229-239.
    [50] Phytopathology, 61 (1971), 600-610.
    [51] Nonlinear Anal. RWA, 9 (2008), 1714-1726.
    [52] Discrete Dyn. Nat. Soc., 2008 (2008), 16pp.
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  • © 2015 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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