Uniqueness and stability of periodic solutions for an interactive wild and Wolbachia-infected male mosquito model

Abstract

We investigate a mosquito population suppression model, which includes the release of Wolbachia-infected males causing incomplete cytoplasmic incompatibility (CI). The model consists of two sub-equations by considering the density-dependent birth rate of wild mosquitoes. By assuming the release waiting period T is larger than the sexual lifespan of Wolbachia-infected males, we derive four thresholds: the CI intensity threshold , the release amount thresholds and , and the waiting period threshold . From a biological view, we assume throughout the paper. When , we prove the origin is locally asymptotically stable iff , and the model admits a unique T-periodic solution iff , which is globally asymptotically stable. When , we show the origin is globally asymptotically stable iff , and the model has a unique T-periodic solution iff , which is globally asymptotically stable. Our theoretical results are confirmed by numerical simulations.