Quantifying the survival uncertainty of <i>Wolbachia</i>-infected mosquitoes in a spatial model

Martin Strugarek; Nicolas Vauchelet; Jorge P. Zubelli; Martin Strugarek; Nicolas Vauchelet; Jorge P. Zubelli

doi:10.3934/mbe.2018043

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 4: 961-991. doi: 10.3934/mbe.2018043

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Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model

1.
AgroParisTech, 16 rue Claude Bernard, 75231 Paris Cedex 05, France
2.
Sorbonne Université, Université Paris-Diderot SPC, CNRS, INRIA, Laboratoire Jacques-Louis Lions, équipe Mamba, F-75005 Paris, France
3.
LAGA - UMR 7539 Institut Galilée, Université Paris 13, 99, avenue Jean-Baptiste Clément 93430 Villetaneuse, France
4.
IMPA, Estrada Dona Castorina, 110 Jardim Botânico 22460-320, Rio de Janeiro, RJ, Brazil

Received: 24 July 2017 Accepted: 03 January 2018 Published: 01 August 2018
MSC : Primary: 35K57, 35B40, 92D25; Secondary: 60H30

Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past years for fighting vector-borne diseases such as dengue, chikungunya and zika. Several strains of this bacterium cause cytoplasmic incompatibility (CI) and can also affect their host's fecundity or lifespan, while highly reducing vector competence for the main arboviruses. We consider and answer the following questions: 1) what should be the initial condition (i.e. size of the initial mosquito population) to have invasion with one mosquito release source? We note that it is hard to have an invasion in such case. 2) How many release points does one need to have sufficiently high probability of invasion? 3) What happens if one accounts for uncertainty in the release protocol (e.g. unequal spacing among release points)? We build a framework based on existing reaction-diffusion models for the uncertainty quantification in this context, obtain both theoretical and numerical lower bounds for the probability of release success and give new quantitative results on the one dimensional case.
- Reaction-diffusion equation,
- Wolbachia,
- uncertainty quantification,
- population replacement,
- mosquito release protocol
Citation: Martin Strugarek, Nicolas Vauchelet, Jorge P. Zubelli. Quantifying the survival uncertainty of Wolbachia-infected mosquitoes in a spatial model[J]. Mathematical Biosciences and Engineering, 2018, 15(4): 961-991. doi: 10.3934/mbe.2018043

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Abstract

Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past years for fighting vector-borne diseases such as dengue, chikungunya and zika. Several strains of this bacterium cause cytoplasmic incompatibility (CI) and can also affect their host's fecundity or lifespan, while highly reducing vector competence for the main arboviruses. We consider and answer the following questions: 1) what should be the initial condition (i.e. size of the initial mosquito population) to have invasion with one mosquito release source? We note that it is hard to have an invasion in such case. 2) How many release points does one need to have sufficiently high probability of invasion? 3) What happens if one accounts for uncertainty in the release protocol (e.g. unequal spacing among release points)? We build a framework based on existing reaction-diffusion models for the uncertainty quantification in this context, obtain both theoretical and numerical lower bounds for the probability of release success and give new quantitative results on the one dimensional case.

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