Resistant Pest Control Of The Development Of The Research Of The Model

Pest control has attracted great attentions of department of ecological agricul-ture. Many factors including timing of pesticide applications and the number of natural enemies to be released can affect the successful of pest control, and those can be investigated by employing mathematical models. In recent years, lots of scholars have studied pest control models with pesticide applications and integrated pest management strategies by using impulsive differential equation. However, all those works ignored the effects of the development of pest resistance to pesticides on the pest control.Pest resistance to pesticides, as one of the side effects associated with the use of chemicals, has received great attention in recent years. The resistance can be divided into acquired resistance which relates to the accumulation of resistance gene and induced resistance which relates to the times and dosages of pesticide appli-cations. One method to control pest after a pest species develops resistance to a particular pesticide is to switch pesticides. Thus, it is essential to consider resistance development into pulsed pest control models to address how does pest resistance af-fect pest control? When should farmers switch pesticides? which factors affect the evolution of pesticide resistance? etc.Assuming that the growth of pest population follows the laws of Logistic growth, the simplest pest control model with pulsed pesticide applications can be described as follows where Tk(k=0.1.2…) denotes impulsive point series at which pesticides are ap-plied, q represents the survival rate of pest after pesticide applications. In this thesis, constant survival rate q is replaced by a function q(t) due to evolution of pest resistance and periodically switching the type of pesticide is described by the periodically changing the survival rate of pest. Consequently, we develop a kind of pulsed pest control model with acquired resistance development and two kinds of pulsed pest control models with induced resistance development. For example, one of the pulsed pest control model with induced resistance development is as follows where nTp(n=0,1,2…) is impulsive point series at which pesticide switching strategy is applied, p denotes the number of each pesticide class applied, k mod p means periodically switching pesticides so the effectiveness of pesticide changed pe-riodically. Here if we do not consider the effects of times on resistance development, i.e., delete the term k mod p, then the model is a pulsed pest control model with acquired resistance development. We have analyzed the dynamics of each model by using the theory of impulsive differential equations, and the threshold values which determine the stability of’pest-eradication’ solution is provided. Moreover, the effects of parameters on The threshold conditions are studied by employing both analytical and numerical techniques, and we have obtained the optimal number of each pesticide used which guarantees the shortest time to eradicate pests.Further, we extend the single chemical control model into integrated pest man-agement model, and then by using the comparison theorem on impulsive differential equations we have obtained the condition that guarantees the existence and global attractivity of ’pest-eradication’ periodic solution and analysis the effects of param-eters on threshold values. Finally, we determine the economic threshold according to the survival rate of pest, then we develop a state-dependent impulsive model with resistance development. The modelling methods and conclusions obtained in this thesis can provide a basis for the study of resistance development on other field and the design of more reasonable pest control strategy.