A study of integrated pest management models with instantaneous and non-instantaneous impulse effects

The occurrence of pests and diseases during agricultural production affects the quality and quantity of agricultural products. It is important to evaluate the impact of various factors on pests to achieve optimal results of integrated pest management (IPM) during its implementation. In this paper, we considered the transient and non-transient effects of chemical control on pests and the effects on natural enemies at different times, and developed a corresponding pest control model. Detailed studies and comparisons were conducted for spraying pesticides either more or less frequently as compared to strategies for releasing natural enemies. The threshold conditions for global asymptotic stabilization of the pest extinction period solution was obtained. Using two-parameter and sensitivity analysis techniques, the parameters affecting the variation of the threshold were discussed. By comparing these two pest control strategies, we found the existence of optimal application and release frequencies. Finally, in order to control pests below the economic threshold level, the state-dependent pest model was numerically investigated. The results show that the presence or absence of chemical control of pests can depend on the values taken for the parameters in the model. Based on this information, pest control experts can make decisions about the best spraying time and the best release rate.

An eco-epidemic model for assessing the application of integrated pest management strategies

Mathematical models have become indispensable tools for analyzing pest control strategies. However, in the realm of pest control studies, the consideration of a plant population being affected by a model that incorporates pests, natural enemies and disease in the pest population has been relatively limited. Therefore, this paper aims to formulate and investigate a hybrid impulsive eco-epidemic model that incorporates disease in the pest population. Initially, we examine the existence and stability of the pest-eradication periodic solution. Subsequently, to explore the impact of chemical and biological control methods, we propose an updated eco-epidemic model that incorporates varying frequencies of pesticide sprays and the release of both infected pests and natural enemies for pest control. We establish threshold values for the susceptible pest eradication periodic solution under different scenarios, illustrating the global attractiveness of this solution. Finally, we discuss the obtained results and suggest potential avenues for future research in this field.

Dynamics of a density-dependent predator-prey biological system with nonlinear impulsive control

Spraying insecticides and releasing natural enemies are two commonly used methods in the integrated pest management strategy. With the rapid development of biotechnology, more and more realistic factors have been considered in the establishment and implementation of the integrated pest management models, such as the limited resources, the mutual restriction between pests and natural enemies, and the monitoring data of agricultural insects. Given these realities, we have proposed a pest-natural enemy integrated management system, which is a nonlinear state-dependent feedback control model. Besides the anti-predator behavior of the pests to the natural enemies is considered, the density dependent killing rate of pests and releasing amount of natural enemies are also introduced into the system. We address the impulsive sets and phase sets of the system in different cases, and the analytic expression of the Poincaré map which is defined in the phase set was investigated. Further we analyze the existence, uniqueness, global stability of order-1 periodic solution. In addition, the existence of periodic solution of order-k (k≥2) is discussed. The theoretical analyses developed here not only show the relationship between the economic threshold and the other key factors related to pest control, but also reveal the complex dynamical behavior induced by the nonlinear impulsive control strategies.

Global dynamics of non-smooth Filippov pest-natural enemy system with constant releasing rate

Modelling integrated pest management (IPM) with a threshold control strategy can be achieved with a non-smooth Filippov dynamical system coupled by an untreated subsystem and a treated subsystem which includes chemical and biological tactics. The releasing constant of natural enemies related to biological control generates the complex dynamics. Comprehensive qualitative analyses reveal that the treated subsystem exists with transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcations, for which the threshold conditions and bifurcation curves are provided. Further, by applying techniques of non-smooth dynamical systems including the Filippov convex method and sliding bifurcation techniques, we first obtain the sliding dynamic equation, and then we analyze the existence and stability of regular/virtual equilibria, pseudo-equilibria, boundary equilibria, sliding segments and sliding bifurcations. In particular, if we choose the economic threshold (ET) as the bifurcation parameter, then interesting dynamical behaviors, including boundary equilibrium → pseudo-homoclinic → touching → buckling → crossing bifurcations, occur in succession. It is interesting to note that although the number of pests in the untreated subsystem could increase and exceed the economic injury level (EIL), the final size could be less than ET and stabilizes at a relative low level due to side effects of the pesticide on natural enemies. However, the side effects can be effectively avoided by increasing the releasing constant, which can maintain the number of pests below the EIL always and thus achieve the control purpose.

[Evaluation of efficiency of traps baited with frequency trembler grid lamps and trap plants for control Heortia vitessoides infectwed in Aquilaria sinensis]

Heortia vitessoides has been a serious defoliating pest of Aquilaria sinensis forests in recent years.The adults displayed strong tropism to the frequency trembler grid lamps and the nectar source plants.The favorite nectar source plants of H.vitessoides adults as the trap plants and the frequency trembler grid lamps in the integrated management of H.vitessoides were studied in the adult eclosion period through both the laboratory and field.The results showed that Kuhnia rosmarnifolia and Santalum album plants showed strong attraction to the H.vitessoides adults, with significant differences among the different nectar source plants.K.rosmarnifolia and S.album as trap plants with board type of planting area to total planting area of 5%-10%, and the frequency trembler grid lamps trapped significantly more adults of H.vitessoides. These results suggested that the frequency trembler grid lamps and trap plants could play an important role in the integrated management of the pest H.vitessoides of A.sinensis.