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Article

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

by 1,2, 1,2 and 1,2,*
1
Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China
2
College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Academic Editor: Juan Benigno Seoane-Sepúlveda
Mathematics 2021, 9(19), 2377; https://doi.org/10.3390/math9192377
Received: 2 September 2021 / Revised: 22 September 2021 / Accepted: 22 September 2021 / Published: 25 September 2021
(This article belongs to the Special Issue Functional Differential Equations and Epidemiological Modelling)
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 α1 during the first N generations, and the release ratio is α2 from the (N+1)-th generation to the T-th generation. Sufficient conditions on the release ratios α1 and α2 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. View Full-Text
Keywords: discrete switching model; Wolbachia; the infection frequency; mosquito population; existence and uniqueness; periodic solutions discrete switching model; Wolbachia; the infection frequency; mosquito population; existence and uniqueness; periodic solutions
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MDPI and ACS Style

Chang, L.; Shi, Y.; Zheng, B. Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model. Mathematics 2021, 9, 2377. https://doi.org/10.3390/math9192377

AMA Style

Chang L, Shi Y, Zheng B. Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model. Mathematics. 2021; 9(19):2377. https://doi.org/10.3390/math9192377

Chicago/Turabian Style

Chang, Lijie, Yantao Shi, and Bo Zheng. 2021. "Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model" Mathematics 9, no. 19: 2377. https://doi.org/10.3390/math9192377

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