Michaela BENEŠOVÁ
Department of Mathematics and Statistics of the Faculty of Science, Masaryk University
Kotlářská 2, 611 37 Brno Czech Republic
misasula@gmail.com
Abstract
The aim of this contribution is to apply methods from optimal control theory to the mathematical modeling of biological pest control. We formulate a pest control strategy for nonlinear Kolmogorov system of n interacting populations by introducing natural enemies as a control function. The sufficient conditions for existence of an optimal feedback control function are based on the fact, that the steady-state solution of the Hamilton-Jacobi-Bellman partial differential equation is a Lyapunov function guaranteeing stability and optimality. We apply those general results to the Lotka-Volterra system with a logistic rate of increase of the prey population and Holling’s second type functional response of the predator population, to illustrate biological control of pest mite in stored grain Acarus siro by predatory mite Cheyletus eruditus.