Loading [Contrib]/a11y/accessibility-menu.js

A new model with delay for mosquito population dynamics

  • 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:

    [1] Liming Cai, Shangbing Ai, Guihong Fan . Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes. Mathematical Biosciences and Engineering, 2018, 15(5): 1181-1202. doi: 10.3934/mbe.2018054
    [2] Zhongcai Zhu, Xiaomei Feng, Xue He, Hongpeng Guo . Mirrored dynamics of a wild mosquito population suppression model with Ricker-type survival probability and time delay. Mathematical Biosciences and Engineering, 2024, 21(2): 1884-1898. doi: 10.3934/mbe.2024083
    [3] Xiaoli Wang, Junping Shi, Guohong Zhang . Bifurcation analysis of a wild and sterile mosquito model. Mathematical Biosciences and Engineering, 2019, 16(5): 3215-3234. doi: 10.3934/mbe.2019160
    [4] Kamaldeen Okuneye, Ahmed Abdelrazec, Abba B. Gumel . Mathematical analysis of a weather-driven model for the population ecology of mosquitoes. Mathematical Biosciences and Engineering, 2018, 15(1): 57-93. doi: 10.3934/mbe.2018003
    [5] Bo Zheng, Lihong Chen, Qiwen Sun . Analyzing the control of dengue by releasing Wolbachia-infected male mosquitoes through a delay differential equation model. Mathematical Biosciences and Engineering, 2019, 16(5): 5531-5550. doi: 10.3934/mbe.2019275
    [6] Yueping Dong, Jianlu Ren, Qihua Huang . Dynamics of a toxin-mediated aquatic population model with delayed toxic responses. Mathematical Biosciences and Engineering, 2020, 17(5): 5907-5924. doi: 10.3934/mbe.2020315
    [7] Fang Liu, Yanfei Du . Spatiotemporal dynamics of a diffusive predator-prey model with delay and Allee effect in predator. Mathematical Biosciences and Engineering, 2023, 20(11): 19372-19400. doi: 10.3934/mbe.2023857
    [8] Fabien Crauste . Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Mathematical Biosciences and Engineering, 2006, 3(2): 325-346. doi: 10.3934/mbe.2006.3.325
    [9] Hongyong Zhao, Yangyang Shi, Xuebing Zhang . Dynamic analysis of a malaria reaction-diffusion model with periodic delays and vector bias. Mathematical Biosciences and Engineering, 2022, 19(3): 2538-2574. doi: 10.3934/mbe.2022117
    [10] Qian Ding, Jian Liu, Zhiming Guo . Dynamics of a malaria infection model with time delay. Mathematical Biosciences and Engineering, 2019, 16(5): 4885-4907. doi: 10.3934/mbe.2019246
  • 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.


    [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
  • This article has been cited by:

    1. Wendi Bao, Yihong Du, Zhigui Lin, Huaiping Zhu, Free boundary models for mosquito range movement driven by climate warming, 2018, 76, 0303-6812, 841, 10.1007/s00285-017-1159-9
    2. Leonid Shaikhet, Stability of the zero and positive equilibria of two connected neoclassical growth models under stochastic perturbations, 2019, 68, 10075704, 86, 10.1016/j.cnsns.2018.07.033
    3. Chunhua Shan, Guihong Fan, Huaiping Zhu, Periodic Phenomena and Driving Mechanisms in Transmission of West Nile Virus with Maturation Time, 2020, 32, 1040-7294, 1003, 10.1007/s10884-019-09758-x
    4. Jemal Mohammed-Awel, Enahoro A. Iboi, Abba B. Gumel, Insecticide resistance and malaria control: A genetics-epidemiology modeling approach, 2020, 325, 00255564, 108368, 10.1016/j.mbs.2020.108368
    5. Marine El Adouzi, Alfonsina Arriaga-Jiménez, Laurent Dormont, Nicolas Barthes, Agathe Labalette, Benoît Lapeyre, Olivier Bonato, Lise Roy, Modulation of feed composition is able to make hens less attractive to the poultry red mite Dermanyssus gallinae, 2020, 147, 0031-1820, 171, 10.1017/S0031182019001379
    6. Leonid Shaikhet, Stability of equilibrium states of a nonlinear delay differential equation with stochastic perturbations, 2017, 27, 10498923, 915, 10.1002/rnc.3605
    7. Haixia Lu, Haitao Song, Huaiping Zhu, A series of population models for Hyphantria cunea with delay and seasonality, 2017, 292, 00255564, 57, 10.1016/j.mbs.2017.07.010
    8. Wanrong Cao, Jia Liang, Yufen Liu, On strong convergence of explicit numerical methods for stochastic delay differential equations under non-global Lipschitz conditions, 2021, 382, 03770427, 113079, 10.1016/j.cam.2020.113079
    9. Leonid Shaikhet, About one method of stability investigation for nonlinear stochastic delay differential equations, 2021, 1049-8923, 10.1002/rnc.5440
    10. Leonid Shaikhet, Stability of equilibria of exponential type system of three differential equations under stochastic perturbations, 2023, 206, 03784754, 105, 10.1016/j.matcom.2022.11.008
    11. A. Yu. Perevaryukha, Simulation of Scenarios of a Deep Population Crisis in a Rapidly Growing Population, 2021, 66, 0006-3509, 974, 10.1134/S0006350921060130
    12. Haitao Song, Dan Tian, Chunhua Shan, Modeling the effect of temperature on dengue virus transmission with periodic delay differential equations, 2020, 17, 1551-0018, 4147, 10.3934/mbe.2020230
    13. Ousmane KOUTOU, Boureima SANGARE, Abou Bakari DIABATE, Mathematical analysis of mosquito population global dynamics using delayed-logistic growth, 2020, 8, 23193786, 1898, 10.26637/MJM0804/0094
    14. Leonid Shaikhet, About stability of equilibria of one system of stochastic delay differential equations with exponential nonlinearity, 2025, 2351-6046, 1, 10.15559/25-VMSTA274
    15. Li Juan, Fan Guihong, Zhang Xianghong, Zhu Huaiping, A Two-Stage Model with Distributed Delay for Mosquito Population Dynamics, 2025, 1040-7294, 10.1007/s10884-025-10431-9
  • Reader Comments
  • © 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)
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(3121) PDF downloads(570) Cited by(15)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog