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

To control the spread of mosquito-borne diseases, one goal World Mosquito Program’s Wolbachia release method is to replace wild vector mosquitoes with Wolbachia-infected ones, whose capability transmitting diseases has been greatly reduced owing infection. In this paper, we propose a discrete switching model which characterizes strategy including an impulsive and periodic release, where males are released ratio α1 during first N generations, α2 from (N+1)-th generation T-th generation. Sufficient conditions on ratios obtained guarantee existence uniqueness nontrivial solutions model. We aim provide new methods count exact numbers models.