Abstract
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.
Highlights
We have proposed a simple analytical model of pest control formulated in a system of ordinary nonlinear differential equations, which governs the dynamical interaction between plant and pest populations
We have examined the effects of constant, proportional, and saturating proportional release rates on the control performance, where the objective functional of the control problem is to minimize the size of fertile pest insect population jointly with the control efforts
Pontryagin maximum principle has been employed in derivation of necessary optimality conditions, and forward–backward sweep method has been utilized in presenting the numerical solution
Summary
It was reported that the losses range between 17 and 23 percent for wheat, maize, potato and soybean, and about 30 percent for rice. These losses are exacerbated by the threat of climate change as rising temperatures and atmospheric CO2 level as well as changing precipitation pattern affect pest insects population dynamics. A recent study by Food and Agriculture Organization of the United Nations (FAO) [4] alerts that climate change will escalate the risk of pests invasion in agricultural and forestry ecosystems, causing loss of 40 percent of crop production and annually costing the global economy at least USD70 billion
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