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 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.
Highlights
Discrete Switching Model.The global incidence of dengue is placing more than 50% of the world’s population at risk, and affects more than 100 countries around the world [1]
As a mosquito-borne disease, dengue viruses are transmitted through the bites of infected Aedes female mosquitoes, including Aedes aegypti and Aedes albopictus, which act as the main vectors of dengue
Motivated by the experimental observation in [7] that supplemental male release in every generation can accelerate the Wolbachia invasion, we develop a general discrete model which is based on the classic models in [11,12,13,14,15,16], which focused on Wolbachia spread dynamics in cage mosquito populations without supplemental releases
Summary
Motivated by the experimental observation in [7] that supplemental male release in every generation can accelerate the Wolbachia invasion, we develop a general discrete model which is based on the classic models in [11,12,13,14,15,16], which focused on Wolbachia spread dynamics in cage mosquito populations without supplemental releases All these discrete models only include a one-time release of both Wolbachia-infected females and males, which generated an unstable equilibrium, below which the Wolbachia infections will disappear, and above which, Wolbachia invasion is successful.
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