Population Diffusion Of Pest Control

Pest control is needed in the development of agriculture production. Generally, pest control is carried out by spraying pesticide or releasing the predators period-ically. Integrated pest management is to combine different pest control strategies, such as biological, chemical, mechanical and cultural methods, to reduce pest out-breaks and protect ecological environment. In this paper, we propose the prey-predator system with periodic biological and chemical control and the dispersal of population. The main aim is to investigate the effects of population dispersal among patches, the time of spraying pesticide, the proportion of pests killed and the number of predators released on pest control.In chapter 2, the Lotka-Volterra predator-prey model is extended in a single patch with periodic biological control and chemical control, and the model is attained in the followingSufficient condition is derived for the globally asymptotical stability of the pest-eradication periodic solution by using the theorems about stability of the solution of the impulsive differential equation and the comparison theorem.Generally, there are refuges for the pests in the real world. And pests or preda-tors possibly move among different patches. So the effects of population dispersal among patches should be considered in the pest control. Therefore, in chapter 3, the Lotka-Volterra predator-prey model proposed in Chapter 2 is further extended in k patches with population dispersal among the k patches, and the model is attained in the following Similarly, sufficient conditions are derived for the globally asymptotical stability of the pest-eradication periodic solution on the k patches by using the theorems about stability, matrix theorems and the comparison theorem.In chapter 4, the model extended on two patches is taken as an example to investigate the effects of population dispersal between two patches on pest control. So we consider the modelIn the same way, the sufficient condition of the globally asymptotical stability of the pest-eradication periodic solution on the two patches is obtained by theoretical investigations, and the numerical investigation is given to discuss the effects of pop-ulation dispersal on the pest-eradication periodic solution. And the results indicate that population dispersal is beneficial to pest control for some ranges of dispersal rates, but is harmful for others. At the same time, the numerical simulations are carried out for both populations and some special cases are investigated particularly.In a word, the results obtained by theoretical and numerical investigations clar-ify that the dispersal of pest and predator populations among patches has significant effects on pest control. And these results can help people to design some effective pest control strategies.