In this work, we construct simple models in terms of differential equations for the dynamics of pest populations and their management using biological pest control. For the first model used, the effect of the biological control is modelled by a function of repeated infinite impulses. And, our second model uses a periodic function proportional to the population to model the effect of biological control. In both cases, we present analytical solutions and derive a discrete version of them. Moreover, convergence conditions are given for periodic solutions. Finally, an application of such models is described for diamondback moth in a plot of broccoli to be controlled by the application of biological pesticides and beneficial parasitoids.