Modelling optimal pest control of non-autonomous predator-prey interaction

Abstract

An ecological system comprehended by a pest and  its natural enemy, the predator, is considered. Parameters of system are time dependent in order to accompany their variations associated to climate evolutions. Combining the use of pesticides and of extra supply of food to predators,  we propose the eradication of pest through optimal control having those two measures as controls. Is established that the resulting problem has a unique solution. Uniqueness is obtained on the whole interval using a  recursive argument. The usefulness of model to tackle the pest population is backed by numerical simulation results.