In recent years, the Asian gall wasp Dryocosmus kuriphilus has invaded chestnut trees and significantly affected the Portuguese chestnut production. Studies in other countries, such as Japan or Italy, have shown that the parasitoid Torymus sinensis can successfully achieve biological control of D. kuriphilus. Mathematical models help us to understand the dynamics of the interaction between the pest D. kuriphilus and its parasitoid T. sinensis and, consequently, they can help to implement measures that enhance crop pest management. In this work, the evolution of the density of D. kuriphilus and T. sinensis across time and space is studied through the numerical solution of models that include parameters based on observations made in Portugal. Simultaneous releases of the parasitoid are simulated at various locations and at different times. The results indicate that, in the case of a small and homogeneous orchard, biological control can be effective, but, in the case of extensive domains, the pest control is much more difficult to achieve. In order for biological control to be efficient, it is necessary to implement, in each chestnut-producing region, a collective strategy based on the annual monitoring of infestation levels.
