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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 6: 1395-1410. doi: 10.3934/mbe.2014.11.1395
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A new model with delay for mosquito population dynamics

  • 1.
    Jiangsu Key Laboratory for NSLSCS, School of Mathematical Science, Nanjing Normal University, Nanjing, 210023
  • 2.
    LAboratory of Mathematical Parallel Systems (LAMPS), Centre for Disease Modeling, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3
  • Received: 01 November 2010 Accepted: 29 June 2018 Published: 01 September 2014

  • MSC : Primary: 92D25, 34C60; Secondary: 34C23.

  • In this paper, we formulate a new model with maturation delay formosquito population incorporating the impact of blood meal resourcefor mosquito reproduction. Our results suggest that except for theusual crowded effect for adult mosquitoes, the impact of blood mealresource in a given region determines the mosquito abundance, it isalso important for the population dynamics of mosquito which mayinduce Hopf bifurcation. The existence of a stable periodic solutionis proved both analytically and numerically. The new model formosquito also suggests that the resources for mosquito reproductionshould not be ignored or mixed with the impact of blood mealresources for mosquito survival and both impacts should beconsidered in the model of mosquito population. The impact ofmaturation delay is also analyzed.

    Citation: Hui Wan, Huaiping Zhu. A new model with delay for mosquito population dynamics[J]. Mathematical Biosciences and Engineering, 2014, 11(6): 1395-1410. doi: 10.3934/mbe.2014.11.1395

    Related Papers:

  • In this paper, we formulate a new model with maturation delay formosquito population incorporating the impact of blood meal resourcefor mosquito reproduction. Our results suggest that except for theusual crowded effect for adult mosquitoes, the impact of blood mealresource in a given region determines the mosquito abundance, it isalso important for the population dynamics of mosquito which mayinduce Hopf bifurcation. The existence of a stable periodic solutionis proved both analytically and numerically. The new model formosquito also suggests that the resources for mosquito reproductionshould not be ignored or mixed with the impact of blood mealresources for mosquito survival and both impacts should beconsidered in the model of mosquito population. The impact ofmaturation delay is also analyzed.


    加载中
    [1] J. Theor. Biolo., 241 (2006), 109-119.
    [2] Academic Press, New York, 1963.
    [3] Theor. Population Biol., 22 (1982), 147-176.
    [4] Bull. Math. Biol., 67 (2005), 1107-1133.
    [5] SIAM J. Appl. Math., 67 (2006), 24-45.
    [6] J. Math. Biol., 39 (1999), 332-352.
    [7] Bulletin of Mathematical Biology, 67 (2005), 1157-1172.
    [8] J. Math. Biol., 38 (1999), 220-240.
    [9] Mathematical Biosciences, 150 (1998), 131-151.
    [10] Mathematical Biosciences, 167 (2000), 51-64.
    [11] J. Math. Biol., 35 (1997), 523-544.
    [12] $3^{rd}$ Edition, Heinemann Medical Books, Portsmouth, NH, 1993.
    [13] Journal of Mathematical Biology, 54 (2007), 309-335.
    [14] SIAM J. Appl. Math., 67 (2007), 408-433.
    [15] Springer- Verlag, New York, 1993.
    [16] OIKOS, 66 (1993), 55-65.
    [17] Ann. NY Acad. Sci., 50 (1948), 221-246.
    [18] Academic Press Inc., Boston, 1993.
    [19] Vector Borne and Zoonotic Diseases, 1 (2001), 317-329.
    [20] Journal of Medical Entomology, 44 (2007), 58-764.
    [21] Mathematical and Computer Modelling, 32 (2000), 747-763.
    [22] J. Theor. Biol., 191 (1998), 95-101.
    [23] in Delay Differential Equations and Applications (eds. O. Arino, M. L. Hbid and E. Ait Dads), NATO Sci. Ser. II Math. Phys. Chem., 205, Springer, Dordrecht, 2006, 477-517.
    [24] Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, 1995.
    [25] Correspondance mathématique et physique, 10 (1838), 113-121.
    [26] Proceedings of the Royal Society. London Ser. B, 271 (2004), 501-507.
    [27] "http://en.wikipedia.org/wiki/" target="_blank">http://en.wikipedia.org/wiki/
    [28] "http://www.mosquitoes.org/LifeCycle.html" target="_blank">http://www.mosquitoes.org/LifeCycle.html
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  • © 2014 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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