A modeling framework for biological pest control.

We present an analytic framework where biological pest control can be simulated. Control is enforced through the choice of a time and space dependent function representing the deployment of a species of predators that feed on pests. A sample of different strategies aimed at reducing the presence of pests is considered, evaluated and compared. The strategies explicitly taken into account range, for instance, from the uniform deployment of predators on all the available area over a short/long time interval, to the alternated insertion of predators in different specific regions, to the release of predators in suitably selected regions. The effect of each strategy is measured through a suitably defined cost, essentially representing the total amount of prey present over a given time interval over all the considered region, but the variation in time of the total amount of pests is also evaluated. The analytic framework is provided by an integro-differential hyperbolic-parabolic system of partial differential equations. While prey diffuse according to the usual Laplace operator, predators hunt for prey, moving at finite speed towards regions of higher prey density.