Spatiotemporal dynamics of an insect population in response to chemical substances

Insect pests represent a serious problem for the agriculture. The most popular control technic is the application of insecticide. This method, however, presents serious risks to the human healthy and to the environment so that new approaches, such as the applications of natural repellent, biological control and push–pull strategies, have been attempted. In this paper, we consider a spatially-discrete system described by Coupled Map Lattices to analyze the dynamics of an insect population when some chemical – insecticide or repellent – is spread over the population. The habitat is supposed to have plenty of resources so that insect individuals only move (flee) in response to the chemical concentration. The chemical substance, in turn, spreads by diffusion and by the wind. We show that the escape behavior of the insects and the wind can reduce the effectiveness of the chemical. Furthermore, we present the corresponding continuous equations that describe the system in the macroscopic scale.