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

Mugen Huang; Moxun Tang; Jianshe Yu; Bo Zheng; Mugen Huang; Moxun Tang; Jianshe Yu; Bo Zheng

doi:10.3934/mbe.2019238

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4741-4757. doi: 10.3934/mbe.2019238

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

1.
School of Statistics and Mathematics, Guangdong University of Finance and Economics,Guangzhou 510320, China
2.
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
3.
Center for Applied Mathematics,4College of Mathematics and Information Sciences,Guangzhou University, Guangzhou 510006, China

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.
- mosquito-born diseases,
- Wolbachia,
- cytoplasmic incompatibility,
- mosquito population suppression,
- delay differential equation
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

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Abstract

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.

References

[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, 2^nd 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.

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