Dual effects of additional food supply and threshold control on the dynamics of a Leslie–Gower model with pest herd behavior

Bemisia tabaci is a major agricultural pest and recognized by the United Nations Food and Agriculture Organization (FAO) as the second largest pest in the world. This paper aims to study the management of Bemisia tabaci from theoretical aspects. Firstly, considering the omnivorous nature of natural enemy species and pest herd behavior, a Leslie–Gower type pest-natural enemy model with additional food supply and non-differentiable rational uptake function is put forward, and the effects of additional food supply and aggregation efficiency on the dynamical behavior of the system are analyzed. Secondly, for the slowness of pest control by natural enemy species, a threshold control strategy is adopted to prevent the spread of Bemisia tabaci by spraying a certain intensity of insecticides and releasing a certain number of natural enemies. The complex dynamics of the system induced by the threshold control are discussed such as the existence of predator-extinction periodic solution, the existence and stability of coexisting order-1 periodic solution. Thirdly, from the perspective of cost control, an optimization problem is constructed based on the existence of the order-1 periodic solution, and the optimal control threshold, control strength and control frequency are determined. At last, to illustrate the theoretical results more intuitively, the numerical simulations in MATLAB program are presented to illustrate the effectiveness and practical significance of the control measures. The results of this study provide a reference for the scientific and reasonable management of Bemisia tabaci and is helpful to realize the sustainable development of agricultural production.