Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model

Lijie Chang, Yantao Shi and Bo Zheng
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Lijie Chang: Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
Yantao Shi: Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
Bo Zheng: Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China

Mathematics, 2021, vol. 9, issue 19, 1-13

Abstract: To control the spread of mosquito-borne diseases, one goal of the World Mosquito Program’s Wolbachia release method is to replace wild vector mosquitoes with Wolbachia -infected ones, whose capability of transmitting diseases has been greatly reduced owing to the Wolbachia infection. In this paper, we propose a discrete switching model which characterizes a release strategy including an impulsive and periodic release, where Wolbachia -infected males are released with the release ratio ? 1 during the first N generations, and the release ratio is ? 2 from the ( N + 1 ) -th generation to the T -th generation. Sufficient conditions on the release ratios ? 1 and ? 2 are obtained to guarantee the existence and uniqueness of nontrivial periodic solutions to the discrete switching model. We aim to provide new methods to count the exact numbers of periodic solutions to discrete switching models.

Keywords: discrete switching model; Wolbachia; the infection frequency; mosquito population; existence and uniqueness; periodic solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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