Mathematical Biosciences and Engineering, 2014, 11(6): 1395-1410. doi: 10.3934/mbe.2014.11.1395.

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

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Hopf bifurcation.; reproduction; stability; maturation delay; blood meal resource; Mosquito population

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

References

  • 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, Journal of Mathematical Biology, 2018, 76, 4, 841, 10.1007/s00285-017-1159-9
  • 2. Leonid Shaikhet, Stability of equilibrium states of a nonlinear delay differential equation with stochastic perturbations, International Journal of Robust and Nonlinear Control, 2017, 27, 6, 915, 10.1002/rnc.3605
  • 3. Haixia Lu, Haitao Song, Huaiping Zhu, A series of population models for Hyphantria cunea with delay and seasonality, Mathematical Biosciences, 2017, 292, 57, 10.1016/j.mbs.2017.07.010
  • 4. Leonid Shaikhet, Stability of the zero and positive equilibria of two connected neoclassical growth models under stochastic perturbations, Communications in Nonlinear Science and Numerical Simulation, 2018, 10.1016/j.cnsns.2018.07.033
  • 5. Chunhua Shan, Guihong Fan, Huaiping Zhu, Periodic Phenomena and Driving Mechanisms in Transmission of West Nile Virus with Maturation Time, Journal of Dynamics and Differential Equations, 2019, 10.1007/s10884-019-09758-x

Reader Comments

your name: *   your email: *  

Copyright Info: 2014, Hui Wan, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved