Analysis of impulse release of Wolbachia to control Nilaparvata lugens

Abstract

Brown planthopper Nilaparvata lugens is a serious rice damaging pest and can transmit rice ragged stunt virus. A new biological control method for Nilaparvata lugens by using Wolbachia wStri has been successful in the laboratory. No matter using the strategy of population replacement or the strategy of population suppression to release Nilaparvata lugens infected with wStri, theoretical analysis shows that Nilaparvata lugens infected with wStri may eventually disappear after interacting with the wild Nilaparvata lugens, so the Nilaparvata lugens infected with wStri should be released several times. The question is when and how much to release. In this paper, we propose a population replacement model and a population suppression model with state-dependent impulse release. The existence and stability conditions of the corresponding periodic solutions for these two systems are obtained by applying the theory of semi-continuous dynamical system. We found that the defined evaluation index of wStri release time determines the property of the solutions of the systems. The growth period of Nilaparvata lugens infected with wStri is divided into several stages according to the evaluation index of wStri release time, and the release measures for different stages are put forward, especially the release strategy to make the wild Nilaparvata lugens extinct is discussed. Based on the concept of control degree, a more realistic control goal is also discussed, which is to keep the wild Nilaparvata lugens under a lower level within a finite time. Numerical simulation shows that the effective control has good robustness to the biological parameters of insect, and both strategies can effectively control the wild Nilaparvata lugens.