Modelling and analysis of periodic impulsive releases of the Nilaparvata lugens infected with wStri- Wolbachia

Abstract

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild-$N.lugens$-eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild $N.lugens$ are also given. In addition, the sufficient conditions for the extinction and persistence of the wild $N.lugens$ in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild $N.lugens$, and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions.

Keywords: 00A71; 34A37; 92B05; Nilaparvata lugens; cytoplasmic incompatibility; global stability; periodic release; wStri-Wolbachia.