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Aphids, the sap-sucking insects, often feeding in clusters on new plant growth, have resulted in large amounts of resources and efforts being spent attempting to control their activities. Taking cotton aphids as an example, this paper presents optimal control problems governed by stochastic models with impulsive interferences. Differing from the moment closure equation methods which are computationally intractable when the model contains excessive species, a new computational approach is employed to solve this problem. The key of the approach is to establish a functional relationship between the control variables involving the releasing rates of sterile insects and the spraying rates of pesticide and corresponding states on aphids and sterile aphids. Then the log-linear regression model is proposed to link the control variables with the moments (including the mean and variance) of states. Using training sample simulated from Gillespie algorithm, the regression coefficients for constraints and the objective function are estimated by least squares method. Simulation shows the error of the prediction of this model is relatively low and control results based on regression model are superior to the method based on the moment closure equations in terms of the control cost. Finally, the relative impacts of the prices and area of the field on optimal tactics are explored. [ABSTRACT FROM AUTHOR]

In this work, we consider a logistic fishery model and discuss the selective impulsive harvesting of fish above a certain age or size by incorporating a time delay in the impulsive harvesting term. It is proved that there exists an asymptotically stable positive periodic solution $x^*_{l1}(t)$ when the catchability coefficient h is less than some critical value $h^*_{l}$. It is concluded that $h^*_{l}$ and $x^*_{l1}$ are increasing with respect to l. Simulations shows that the delayed harvesting is advantageous to the sustainability of the population. [ABSTRACT FROM AUTHOR]