Export file:

Format

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

Content

  • Citation Only
  • Citation and Abstract

Establishing Wolbachia in the wild mosquito population: The effects of wind and critical patch size

1 School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China
2 School of Mathematics and Information Technology, Yuncheng University, Yuncheng, Shanxi, 044000, China
3 Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

Special Issues: Mathematical Modeling of Mosquito-Borne Diseases

Releasing mosquitoes with Wolbachia into the wild mosquito population is becoming the very promising strategy to control mosquito-borne infections. To investigate the effects of wind and critical patch size on the Wolbachia establishment in the wild mosquito population, in this paper, we propose a diffusion-reaction-advection system in a heterogeneous environment. By studying the related eigenvalue problems, we derive various conditions under which Wolbachia can fully establish in the entire wild mosquito population. Our findings may provide some useful insights on designing practical releasing strategies to control the mosquito population.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Wolbachia; advection; the minimal patch size; mosquito-borne; heterogeneous environment

Citation: Yunfeng Liu, Guowei Sun, Lin Wang, Zhiming Guo. Establishing Wolbachia in the wild mosquito population: The effects of wind and critical patch size. Mathematical Biosciences and Engineering, 2019, 16(5): 4399-4414. doi: 10.3934/mbe.2019219

References

  • 1. O. J. Brady, P. W. Gething, S. Bhatt, et al., Refining the global spatial limits of dengue virus trans-mission by evidence-based consensus, PLoS Negl. Trop. Dis., 6 (2012), e1760.
  • 2. Dengue Situation Update 453, World Health Organization, (2014), Available from: http://www.wpro.who.int/ emerging diseases/denguebiweekly 02dec2014.pdf.
  • 3. L. M. Schwartz, M. E. Halloran, A. P. Durbin, et al., The dengue vaccine pipeline: Implications for the future of dengue control, Vaccine, 33 (2015), 3293–3298.
  • 4. G. Bian, Y. Xu, P. Lu, et al., The endosymbiotic bacterium Wolbachia induces resistance to dengue virus in Aedes aegypti, PLoS Pathog., 6 (2010), e1000833.
  • 5. H. Dutra, M. Rocha, F. Dias, et al., Wolbachia blocks currently circulating Zika virus isolates Aedes aegypti mosquitoes, Cell Host & Microbe, 19 (2016), 771–774.
  • 6. M. Turelli and A. A. Hoffmann, Rapid spread of an inherited incompatibility factor in California Drosophila, Nature, 353 (1991), 440–442.
  • 7. Z. Xi, C. C. Khoo and S. I. Dobson, Wolbachia establishment and invasion in an Aedes aegypti laboratory population, Science, 310 (2005), 326–328.
  • 8. B. Zheng, M. Tang and J. Yu, Modeling Wolbachia spread in mosquitoes through delay differential equations, SIAM J. Appl. Math., 74 (2014), 743–770.
  • 9. M. Huang, M. Tang and J. Yu, Wolbachia infection dynamics by reaction-diffusion equations, Sci. China Math., 58 (2015), 77–96.
  • 10. L. T. Takahashi, N. A. Maidana, W. C. Ferreira, et al., Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind, Bull. Math. Biol., 67 (2005), 509–528.
  • 11. T. L. Schmidt, N. H. Barton, G. Rašić, et al., Local introduction and heterogeneous spatial spread of dengue-suppressing Wolbachia through an urban population of Aedes aegypti, PLoS Biol., 15 (2017), e2001894.
  • 12. M. Huang, J. Luo, L. Hu, et al., Assessing the efficiency of Wolbachia driven aedes mosquito suppression by delay differential equations, J. Theoret. Biol., 440 (2018), 1–11.
  • 13. J. Yu, Modeling mosquito population suppression based on delay differential equations, SIAM J. Appl. Math., 78 (2018), 3168–3187.
  • 14. B. Zheng, M. Tang, J. Yu, et al., Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission, J. Math. Biol., 76 (2018), 235–263.
  • 15. M. Huang, J. Yu, L. Hu, et al., Qualitative analysis for a Wolbachia infection model with diffusion, Sci. China Math., 59 (2016), 1249–1266.
  • 16. L. Hu, M. Huang, M. Tang, et al., Wolbachia spread dynamics in stochastic environments, Theor. Popul. Biol., 106 (2015), 32–44.
  • 17. L. Cai, S. Ai and J. Li, Dynamics of mosquitoes populations with different strategies for releasing sterile mosquitoes, SIAM J. Appl. Math., 74 (2014), 1786–1809.
  • 18. P. Zhou and X. Zhao, Evolution of passive movement in advective environments: General boundary condition, J. Differ. Equations, 264 (2018), 4176–4198.
  • 19. Y. Lou and P. Zhou, Evolution of dispersal in advective homogeneous environment: the effect of boundary conditions, J. Differ. Equations, 259 (2015), 141–171.
  • 20. R. Cantrell and C. Cosner, Spatial Ecology via Reaction-diffusion Equations, John Wiley & Sons, (2003).
  • 21. P. Zhou and D. Xiao, The diffusive logistic model with a free boundary in heterogeneous environ-ment, J. Differ. Equations, 256 (2014), 1927–1954.

 

Reader Comments

your name: *   your email: *  

© 2019 the Author(s), 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