Optimization process of the integrated plant protection method for dot models

An integrated method of protection against pests of agrocenoses is understood as the complex application of chemical, biological, agrotechnical, mechanical, and other methods of protection against harmful insects. The parameters of the integrated protection method are the level of efficiency of entomophages and the level of harmfulness of pests which are presented in the form of mathematical formulas. The present article discusses the optimal control problems associated with biological systems consisting of three trophic levels “plant – harmful insects – beneficial insects” of the plant protection process taking into account the incoming external resource. For a model biosystem, the necessary conditions for solving the optimization process of plant protection from pests have been formed and substantiated. The Pontryagin maximum principle is proved for optimal control problems associated with model biosystems.