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            <funder>E. Escobar, Hector J. Martinez, and Olga Vasilieva acknowledge financial support from the National Fund for Science, Technology, and Innovation (Autonomous Heritage Fund Francisco José de Caldas) by way of the Research Program No. 1106-852-69523, Contract: CT FP 80740-439-2020 (Colombian Ministry of Science, Technology, and Innovation – Minciencias), Grant ID: CI-71241 (Universidad del Valle). The endorsement obtained from the STIC AmSud Program for regional cooperation (20-STIC-05 NEMBICA project) is gratefully recognized by all authors.</funder>
            <funder>Yves Dumont is (partially) supported by the DST/NRF SARChI Chair in Mathematical Models and Methods in Biosciences and Bioengineering at the University of Pretoria (Grant 82770). Yves Dumont acknowledges the support of DST/NRF Incentive Grant (Grant 119898) and the support of the Conseil Régional de la Réunion, the Conseil Départemental de la Réunion, the European Agricultural Fund for Rural Development (EAFRD) and the Centre de Coopération Internationale en Recherche Agronomique pour le Développement (CIRAD).</funder>
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              <p>Laboratory experiments as well as some field essays have revealed that the intracellular bacterium Wolbachia, deliberately introduced in Aedes spp female mosquitoes, drastically reduces their vector competence for dengue virus and other pathogens. However, female mosquitoes infected with Wolbachia still need to ingest human blood while male mosquitoes, either wild or Wolbachia-carrying, do not bite people. Moreover, Wolbachia-carrying females may transmit the virus to people during blood-feeding, even though with a far less probability than the wild ones. Therefore, massive releases of Wolbachia-carrying females may increase both the nuisance and the epidemiological risk among human residents. In this paper, we propose a sex-structured model of Wolbachia invasion that brings forward the possibility of developing male-biased release strategies of Wolbachia-carriers leading to Wolbachia invasion. Thanks to this model, we study the minimal amount of mosquitoes necessary to complete this task, according to the relative sex-ratio of the released mosquitoes and to the release schedule. We also pay attention to the estimate of the time needed to achieve the ultimate population replacement.</p>
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