Research article Special Issues

The impact of mating competitiveness and incomplete cytoplasmic incompatibility on Wolbachia-driven mosquito population suppressio

  • Received: 28 November 2018 Accepted: 14 May 2019 Published: 27 May 2019
  • To control mosquito-borne diseases such as dengue, malaria, and Zika, Wolbachia-infected male mosquitoes have been released in open areas to suppress wild mosquito population driven by cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment on how the CI intensity $\xi$, and the mating competitiveness $\mu$ of released males relative to wild males, impact the suppression efficacy by a delay differential equation model. Our analysis identifies a threshold CI intensity $\xi_0\in (0, 1)$ as an increasing function of the natural reproduction rate of the wild mosquitoes, and a threshold value $r^*$ for the ratio $r(t)$ between the numbers of released males and wild males. The population suppression fails when $\xi\le \xi_0$, and succeeds when $\xi>\xi_0$ and $r(t)\ge r^*$. Our analyses indicate that $\xi$ plays a more important role than $\mu$ in the population suppression. For instance, a slight decrease of $\xi$ from 1 to 0.92 is more devastating than halving $\mu$ from 1 to 0.5. In our estimation of the optimal starting date for infected male release to target a more than $95\%$ wild population reduction during the peak season of dengue in Guangzhou, we find that the optimal date is almost independent of $\mu$ but is sensitive to $\xi$. If CI is complete, then starting about two months ahead can be an optimal option for less financial and labor costs. A slight reduction in the CI intensity requires a considerably earlier starting date.

    Citation: Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. The impact of mating competitiveness and incomplete cytoplasmic incompatibility on Wolbachia-driven mosquito population suppressio[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4741-4757. doi: 10.3934/mbe.2019238

    Related Papers:

  • To control mosquito-borne diseases such as dengue, malaria, and Zika, Wolbachia-infected male mosquitoes have been released in open areas to suppress wild mosquito population driven by cytoplasmic incompatibility (CI). In this work, we initiate a preliminary assessment on how the CI intensity $\xi$, and the mating competitiveness $\mu$ of released males relative to wild males, impact the suppression efficacy by a delay differential equation model. Our analysis identifies a threshold CI intensity $\xi_0\in (0, 1)$ as an increasing function of the natural reproduction rate of the wild mosquitoes, and a threshold value $r^*$ for the ratio $r(t)$ between the numbers of released males and wild males. The population suppression fails when $\xi\le \xi_0$, and succeeds when $\xi>\xi_0$ and $r(t)\ge r^*$. Our analyses indicate that $\xi$ plays a more important role than $\mu$ in the population suppression. For instance, a slight decrease of $\xi$ from 1 to 0.92 is more devastating than halving $\mu$ from 1 to 0.5. In our estimation of the optimal starting date for infected male release to target a more than $95\%$ wild population reduction during the peak season of dengue in Guangzhou, we find that the optimal date is almost independent of $\mu$ but is sensitive to $\xi$. If CI is complete, then starting about two months ahead can be an optimal option for less financial and labor costs. A slight reduction in the CI intensity requires a considerably earlier starting date.


    加载中


    [1] S. Bhatt, P. W. Gething, O. J. Brady, et al., The global distribution and burden of dengue, Nature, 496 (2013), 504–507.
    [2] N.G.Gratz, Critical review of the vector status of Aedes albopictus, Med.Vet.Entomol., 18(2004), 215–227.
    [3] H. Lin, T. Liu, T. Song, et al., Community involvement in dengue outbreak control: An integrated rigorous intervention strategy, PLoS Negl. Trop. Dis., 10 (2016), e0004919.
    [4] B. Zheng, J. Yu, Z. Xi, et al., The annual abundance of dengue and Zika vector Aedes albopictus and its stubbornness to suppression, Ecol. Model., 387 (2018), 38–48.
    [5] Z. Xi, C. C. Khoo and S. L. Dobson, Wolbachia establishment and invasion in an Aedes aegypti laboratory population, Science, 310 (2005), 326–328.
    [6] T. Walker, P. H. Johnson, L. A. Moreika, et al., The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations, Nature, 476 (2011), 450–453.
    [7] E. Waltz, US reviews plan to infect mosquitoes with bacteria to stop disease, Nature, 89 (2016), 450–451.
    [8] D. Zhang, X. Zheng, Z. Xi, et al., Combining the sterile insect technique with the incompatible insect technique: I-impact of Wolbachia infection on the fitness of triple- and double-infected strains of Aedes albopictus, PLoS One, 10 (2015), e0121126.
    [9] M. S. Blagrove, C. Arias-Goata, A. B. Failloux, et al., Wolbachia strain wMel induces cytoplasmic incompatibility and blocks dengue transmission in Aedes albopictus, Proc. Natl. Acad. Sci. USA, 109 (2012), 255–260.
    [10] A. A. Hoffmann, B. L. Montgomery, J. Popovici, et al., Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission, Nature, 476 (2011), 454–457.
    [11] D. Zhang, R. S. Lees, Z. Xi, et al., Combining the sterile insect technique with Wolbachia-based approaches: II-a safer approach to Aedes albopictus population suppression programmes, designed to minimize the consequences of inadvertent female release, PLoS One, 10 (2015), e1427.
    [12] X. Wang, S. Tang and R. A. Cheke, A stage structured mosquito model incorporating effects of precipitation and daily temperature fluctuations, J. Theor. Biol., 411 (2016), 27–36.
    [13] X. Zhang, S. Tang, R. A. Cheke, et al., Modeling the effects of augmentation strategies on the control of dengue fever with an impulsive differential equation, Bull. Math. Biol., 78 (2016), 1968–2010.
    [14] B. Zheng, M. Tang and J. Yu, Modeling Wolbachia spread in mosquitoes through delay differential equation, SIAM J. Appl. Math., 74 (2014), 743–770.
    [15] M. Huang, M. Tang and J. Yu, Wolbachia infection dynamics by reaction-diffusion equations, Sci. China Math., 58 (2015), 77–96.
    [16] M. Huang, J. Yu, L. Hu, et al., Qualitative analysis for a Wolbachia infection model with diffusion, Sci. China Math., 59 (2016), 1249–1266.
    [17] L. Hu, M. Huang, M. Tang, et al., Wolbachia spread dynamics in stochastic environments, Theor. Popul. Biol., 106 (2015), 32–44.
    [18] L. Hu, M. Huang, M. Tang, et al., Wolbachia spread dynamics in multi-regimes of environmental conditions, J. Theor. Biol., 462 (2019), 247–258.
    [19] L. Hu, M. Tang, Z. Wu, et al., The threshold infection level for Wolbachia invasion in random environments, J. Diff. Equ., 266 (2019), 4377–4393.
    [20] B. Zheng, W. Guo, L. Hu, et al., Complex Wolbachia infection dynamics in mosquitoes with imperfect maternal transmission, Math. Biosci. Eng., 15 (2018), 523–541.
    [21] B. Zheng, M. Tang, J. Yu, et al., Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission, J. Math. Biol., 76 (2018), 235–263.
    [22] B. Zheng and J. Yu, Characterization of Wolbachia enhancing domain in mosquitoes with imper-fect maternal transmission, J. Biol. Dyn., 12 (2018), 596–610.
    [23] M. Huang, L. Hu and B. Zheng, Comparing the efficiency of Wolbachia driven Aedes mosquito suppression strategies, J. Appl. Anal. Comput., 9 (2019), 1–20.
    [24] M. Huang, J. Lou, L. Hu, et al., Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations, J. Theor. Biol., 440 (2018), 1–11.
    [25] J. Yu, Modeling mosquito population suppression based on delay differential equations, SIAM J. Appl. Math., 78 (2018), 3168–3187.
    [26] B. Zheng, X. Liu, M. Tang, et al., Use of age-stage structural models to seek optimal Wolbachia-infected male mosquito releases for mosquito-borne disease control, J. Theor. Biol., 472 (2019), 95–109.
    [27] Y. Li, F. Kamara, G. Zhou, et al., Urbanization increases Aedes albopictus larval habitats and accelerates mosquito development and survivorship, PLoS Negl. Trop. Dis., 8 (2014), e3301.
    [28] F. Liu, C. Zhou and P. Lin, Studies on the population ecology of Aedes albopictus 5. The sea-sonal abundance of natural population of Aedes albopictus in Guangzhou, Acta Sci. Natur. Univ. Sunyatseni, 29 (1990), 118–122.
    [29] F. Liu, C. Yao, P. Lin, et al., Studies on life table of the natural population of Aedes albopictus, Acta Sci. Natur. Univ. Sunyatseni, 31 (1992), 84–93.
    [30] H. I. Freedman, Deterministic mathematical models in population ecology, 2nd edition, HIFR Consulting LTD, Edmonton, 1987.
    [31] H. L. Smith, An introduction to delay differential equations with applications to life sciences, Springer-Verlag, New York, 2011.
    [32] S. Lee, Development of eggs, larvae and pupae of Aedes albopictus (Skuse) (Diptera: Culicidae), Chinese J. Entomol., 14 (1994), 13–32.
    [33] Z. Liu, Y. Zhang and Y. Yang, Population dynamics of Aedes (Stegomyia) albopictus (Skuse) under laboratory conditions, Acta Entomol. Sin., 28 (1985), 274–280.
    [34] L. Zhang, L. Tan, H. Ai, et al., Laboratory and field studies on the oviposition pattern of Aedes albopictus, Acta Parasitol. Et. Med. Entomol. Sin., 16 (2009), 219–223.
    [35] Z. Zhong and G. He, The life table of laboratory Aedes albopictus under various temperatures, Academic J. Sun Yat-sen Univ. Med. Sci., 9 (1988), 35–39.
    [36] Y. Wang, X. Liu, C. Li, et al., A survey of insecticide resistance in Aedes albopictus (Diptera: Culicidae) during a 2014 dengue fever outbreak in Guangzhou, China, J. Econ. Entomol., 110 (2017), 239–244.
  • Reader Comments
  • © 2019 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(3709) PDF downloads(577) Cited by(12)

Article outline

Figures and Tables

Figures(3)  /  Tables(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog