We propose an impulsive biological pest control of the sugarcane borer Diatraea saccharalis by its egg parasitoid Trichogramma galloi based on a mathematical model in which the sugarcane borer is represented by the egg and larval stages, and the parasitoid is considered in terms of the parasitized eggs. By using the Floquet theory and the small amplitude perturbation method, we show that there exists a globally asymptotically stable pest-eradication periodic solution when some conditions hold. The numerical simulations show that the impulsive release of parasitoids provides reliable strategies of the biological pest control of the sugarcane borer.
We formulate an infinite-time quadratic functional minimization problem of Aedes aegypti mosquito population. Three techniques of mosquito population management, chemical insecticide control, sterile insect technique control, and environmental carrying capacity reduction, are combined in order to obtain the most sustainable strategy to reduce mosquito population and consequently dengue disease. The solution of the optimization control problem is based on the ideas of the Dynamic Programming and Lyapunov Stability using State-Dependent Riccati Equation (SDRE) control method. Different scenarios are analyzed combining three mentioned population management efforts in order to assess the most sustainable policy to reduce the mosquito population.
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