This work puts forward a dynamical population model to qualitatively reproduce the phenomena of apparent competition and apparent mutualism found in an experiment with two arthropods being attacked by a predator in a context of pest biological control in greenhouse crops. The two agricultural pests consist of one species of thrips (Frankliniella occidentalis (Pergande 1895)) and one species of whiteflies (Trialeurodes vaporariorum Westwood, 1956), and the shared predator is a predatory mite (Amblyseius swirskii Athias-Herriot, 1962). The predatory mite is the biocontrol agent employed in order to achieve the biological control. The proposed model successfully reproduces this density mediated indirect interactions between pests when their carrying capacities are increased. Moreover, the pests' final population levels may depend on their initial densities and those of their predator. With these results, the proposed model may have the potential to assess whether these indirect pest interactions disrupt or enhance biological control. Additionally, it can also be used as an ancillary tool to theoretically assess the effects of pest biocontrol strategies in the referred experimental setup.