Study on a switching model with stage structure for the integrated management of Bactericera gobica Loginova

On the basis of the biological characteristics of Bactericera gobica Loginova, this paper classifies its population into nymphs and adults. By comprehensively considering both chemical and biological control strategies, combining the instantaneous and noninstantaneous residual effects of pesticides on nymphs and adults of B. gobica at different stages, as well as the predation effects of dominant natural enemies, a stage structured switching model for the integrated management of B. gobica is established. We analyzed the dynamic properties of the proposed model and theoretically demonstrated sufficient conditions for the existence and global asymptotic stability of the periodic extinction solution of B. gobica. Numerically, we investigated the effects of the pulse period and release amount of natural enemies on B. gobica and observed that the system exhibits various complex dynamical behaviors, including periodic solutions, period-doubling bifurcations, and chaos. Additionally, through scatter plots, contour maps, and sensitivity analyses, we demonstrated the impact of key parameters on the extinction threshold of B. gobica. These results indicate that shortening the pulse period of natural enemy release, increasing the release quantity, and selecting appropriate pesticide application times significantly enhance pest control. However, frequent pesticide spraying does not necessarily yield optimal outcomes, emphasizing the importance of rationally planning pesticide application frequency. Finally, to maintain B. gobica populations below the economic threshold, we established a state-dependent integrated pest management switching model. These findings reveal that factors such as the release period and quantity of natural enemies, initial conditions, and the noninstantaneous killing rate of pesticides on B. gobica nymphs substantially influence the frequency of pesticide application.