Existence and stability of periodic solutions in a mosquito population suppression model with time delay

Abstract

By including the maturation period τ of wild mosquitoes, we develop a delay differential equation model to study the suppression of wild mosquito population by releasing Wolbachia-infected male mosquitoes with a release period T=τ/m, where m is a positive integer. We obtain sufficient conditions for non-existence of periodic solutions and existence of a unique or exactly two periodic solutions by taking the initial function as a solution to the delay-free model. We prove the global asymptotic stability of the unique periodic solution, and that one periodic solution is stable and the other is unstable when there are two periodic solutions.