Mathematical Model of Pest Control Using Different Release Rates of Sterile Insects and Natural Enemies

In the framework of integrated pest management, biological control through the use of living organisms plays important roles in suppressing pest populations. In this paper, the complex interaction between plants and pest insects is examined under the intervention of natural enemies releases coupled with sterile insects technique. A set of nonlinear ordinary differential equations is developed in terms of optimal control model considering characteristics of populations involved. Optimal control measures are sought in such a way they minimize the pest density simultaneously with the control efforts. Three different strategies relating to the release rate of sterile insects and predators as natural enemies, namely, constant, proportional, and saturating proportional release rates, are examined for the attainability of control objective. The necessary optimality conditions of the control problem are derived by using Pontryagin maximum principle, and the forward–backward sweep method is then implemented to numerically calculate the optimal solution. It is shown that, in an environment consisting of rice plants and brown planthoppers as pests, the releases of sterile planthoppers and ladybeetles as natural enemies can deteriorate the pest density and thus increase the plant biomass. The release of sterile insects with proportional rate and the release of natural enemies with constant rate are found to be the most cost-effective strategy in controlling pest insects. This strategy successfully decreases the pest population about 35 percent, and thus increases the plant density by 13 percent during control implementation.

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.

AN INTEGRATED PEST MANAGEMENT MODEL WITH DOSE-RESPONSE EFFECT OF PESTICIDES

Considering the delayed response to pesticide applications and the long-term residual effects of pesticides after the deployment of a pest management strategy, this paper develops a pollutant-discharge model to simulate pesticide spraying and analyze the effect of releasing natural enemies of the pest. The following two different control strategies are discussed: (1) the frequency of spraying pesticides is higher than that of releasing natural enemies, and (2) the frequency of releasing natural enemies is higher than that of spraying pesticides. For different control strategies, the sufficient conditions of locally asymptotic stability and globally asymptotic stability of the pest-eradication periodic solution are obtained. Using numerical simulations, we analyze the sensitivity of the threshold condition with respect to the parameters, identify the major factors affecting pest control and provide guidance for decision-making in pest management. Finally, we compare the control strategies and analyze which strategy is optimal as the most significant control parameters are varying.