Study Of Hybrid Models Based On Integrated Pest Management

Chemical control and biological control are two essential tactics in integrated pest management (IPM), which are usually used in combination in pest control. However, chemical control may have unexpected consequences, such as pesticides not only act on the pest species but also act on their natural enemies, which results in pest population outbreak again. Thus, how to use chemical control and biological control reasonably in combination have taken great attentions to department of ecological agriculture. Moreover, in many cases, pesticides have the delayed response and residual effects on pests, and those factors affect the successful pest control. It is well known that the longer residual effects and shorter delayed effects of pesticides on pest, the more to successful pest control. Therefore, how to use delayed and residual effects of pesticides is an important issue for pest control.Recently, more and more pests have developed resistance to pesticides, and this situation have challenged on successful pest control. In order to combat the evolution of pest resistance some experts have proposed a number of principles for delaying the growth of resistance or avoiding it entirely. These principles include switching or rotating between different pesticide; Avoiding unnecessary pesticide spraying by using non-chemical control techniques within the concept of IPM. When employing pesticide switches or rotations to fight the development of pest resistance, the key issues are:What is justification for pesticide switching? And what is the optimal fre-quency of pesticide spraying? In the combination of chemical and biological control tactics, what is the optimal rates of natural enemy releases with the development of pesticide resistance?In order to answer above questions, in chapter2the impulsive differential e-quations of hybrid dynamical models are used to model IPM and the residual effects of pesticides have been described by piecewise-continuous functions. The global attractive for pest free periodic solutions have been analyzed and the threshold con-ditions are given for the three different cases. Residual effects of the pesticide on the pest and on its natural enemies, the frequency of pesticide applications and the fre-quency of natural enemy releases on the threshold conditions are investigated with regard to the extinction of pest population or resurgence resulting from pulses of pesticide applications and predator releases. The key control parameters which are most significantly related to threshold values are investigated by numerical analysis. The results combined with Volterra’s principle confirm that repeated use of the same pesticide can lead to target pest resurgence, when the pesticide has a strong effect on the natural enemies. The results also indicate that there exists an optimal frequency of pesticide applications which can control the pest population most effectively.Based on the models developed in chapter2, the delayed effects of pesticides has been considered and studied in chapter3. For the model with fixed pulse actions, the threshold conditions for the pest eradication are investigated under three different cases, and the effects of residual and delayed response to pesticide applications, the frequency of pesticide applications and the frequency of natural enemy releases on the threshold values are discussed in detail. The results indicate that there exists an optimal frequency of pesticide applications or an optimal releasing period which maximizes the threshold value. For the model with unfixed pulse-actions and EIL, three different pest control tactics are investigated and compared, and the effects of the pesticide killing efficiency rate, delayed response rate and decay rate on the frequency of control actions and the pest outbreak period are also investigated numerically. The results confirm that the IPM is the optimal control strategy.In chapter4, a novel pest growth model incorporating the development of pest resistance and pulse spraying of pesticides are developed and investigated. Under pesticide switching tactics, three switching methods are introduced. The optimal switching time under those three pesticide switching methods and the optimal choice are discussed under different conditions. Our results suggest that either the efficien-cy of pesticides-guided or EIL-guided method is the optimal pesticide switching strategy, depending on the period of pesticide applications. Furthermore, we also developed the model with IPM such as combining chemical and biological control for fighting pesticide resistance. The global attractive of pest free periodic solutions have been analyzed and the threshold conditions for pest eradication are given for two different cases, then the number of natural enemies should be released when threshold conditions to ensure pest eradication under two different control tactics are reached. Our results show that the number of natural enemies to be released for the extinction of the pest population in the presence of increasing pesticide re-sistance can be determined analytically and depends on the cumulative number of dead natural enemies before the next scheduled release time.The modeling ideals, analytical techniques and numerical methods developed in this article can be employed to investigate the general pest control models with IPM strategy. The results obtained in this work may help in the design of an optimal pest control strategy for department of ecological agriculture.