Mathematical Study On A Kind Of Pest Management SI Model With Residual Effects Of Pesticides

With the development of society and the progress of science and technology, pest management increasingly becomes the common research topics by all countries around the world. At present, chemical control and biological control are often used in pest control. In this paper, it supposes that the pest population is divided into susceptible pests and infected pests, and natural enemies only predate the susceptible pests. By applying the epidemic model to model the process of pest management, a kind of pest management SI model with pesticides that have residual effects and different frequency are proposed and studied. And the dynamics of the model with different pesticides functions are systematically discussed. The methods and conclusions obtained in this paper can provide a reliable strategy basis for integrated pest management problems.In Chapter 1, relevant preliminaries are introduced.In Chapter 2, based on the impulsive differential equations, the SI pest control model with chemical and biological control are proposed, and the residual effects of pesticides are introduced in the model. In this chapter, the effect function pesticide is described by step function, the following two different control strategies are considered: spraying pesticide more frequent than the release of the infected pests and natural enemies or the release of the infected pests and natural enemies more frequent than spraying pesticide. By using the relevant theory and analytic methods of impulsive differential equation, the sufficient conditions of existence and global attractiveness of pest-eradication periodic solution are obtained.In Chapter 3, considering the pesticides have a decay effect with time going by, the pesticides functions with residual effects in chapter 2 are changed into continuous exponential functions. The dynamics under two different control strategies are also studied. The sufficient conditions of existence and global attractiveness of pest-eradication periodic solution are given. In addition, in this chapter, the influence and sensibility of the main parameters to the threshold conditions are analyzed by numerical analysis methods. It is obtained that the killing efficiency rates and decay rates of the pesticide effect function of the susceptible pests play a crucial role in the pest control, and the optimal frequency of pesticide applications are obtained.