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One discrete dynamical model on the Wolbachia infection frequency in mosquito populations

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How to prevent and control the outbreak of mosquito-borne diseases, such as malaria, dengue fever and Zika, is an urgent worldwide public health problem. The most conventional method for the control of these diseases is to directly kill mosquitoes by spraying insecticides or removing their breeding sites. However, the traditional method is not effective enough to keep the mosquito density below the epidemic risk threshold. With promising results international, the World Mosquito Program’s Wolbachia method is helping to reduce the occurrence of diseases transmitted by mosquitoes. In this paper, we introduce a generalized discrete model to study the dynamics of the Wolbachia infection frequency in mosquito populations where infected mosquitoes are impulsively released. This generalized model covers all the relevant existing models since 1959 as some special cases. After summarizing known results of discrete models deduced from the generalized one, we put forward some interesting open questions to be further investigated for the periodic impulsive releases.

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This work was supported by National Natural Science Foundation of China (Grant Nos. 11971127, 12071095 and 11631005) and the Changjiang Scholars Program and Program for Innovative Research Team in University (Grant No. IRT_16R16).

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Correspondence to Jianshe Yu.

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Zheng, B., Li, J. & Yu, J. One discrete dynamical model on the Wolbachia infection frequency in mosquito populations. Sci. China Math. 65, 1749–1764 (2022).

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