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

^{setArticleTag('','1,2','1','strugarek@ljll.math.upmc.fr');},^{setArticleTag('','3','','');},^{setArticleTag('','4','','');}

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: , Accepted: , Published:

Artificial releases of *Wolbachia*-infected *Aedes* mosquitoes have been under study in the past yearsfor 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 successand give new quantitative results on the one dimensional case.

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