An SI integrated pest management model with pesticide resistance to susceptible pests

In this paper, epidemic diseases among pests are assumed to occur, so pests are divided into susceptible pests and infected pests, and only susceptible pests are harmful to crops. Considering spraying pesticides and releasing of natural enemies and infected pests to control pests, as well as the long-term application of the same pesticide to induce resistance, an integrated pest management with pesticide resistance is established. The pollution emission model is introduced to model the action process of pesticides, which well reflects its residual and delay effects. By using comparison theorem of impulsive differential equation and analysis method, the threshold condition for eradication of susceptible pests is obtained. Then we analyze the frequency of spraying pesticide on the success of pests control. It shows that it is not that the more frequently pesticides are applied, the better the result of the susceptible pests control is. From the sensitivity analysis, the key factors on the threshold are obtained. Finally, the strategies to control susceptible pests are given, including switching pesticides and releasing infected pests and natural enemies elastically.