Impulsive spatial control of invading pests by generalist predators (Q2922512)

The authors adapt an existing ODE model of integrated pest management via time-dependent impulsive controls [\textit{B. Liu} et al., J. Comput. Appl. Math. 193, No. 1, 347--362 (2006; Zbl 1089.92060)] to account for the effects of spatial diffusion. One of the main aspects is the eradication of pest in a reaction-diffusion predator-pest (parasitoid-pest) model by augmenting the action of the predator (parasitoid) through the use of impulsive spatial controls. The motivating example is the control of \textit{Cameraria Ohridella} (horse chestnut leaf miner) through the use of its generalist parasitoids and the yearly destruction of affected leaves.NEWLINENEWLINEIt is observed, via the use of a comparison principle for parabolic equations with nonlocal terms and the Krein-Rutman theorem, that the spatial control of pest, understood as the convergence to \(0\) of the \(L^\infty\) norm, can be achieved if a principal eigenvalue of a certain nonselfadjoint operator is large enough. Further comments regarding possible extensions of the model to incorporate additional controls, estimations of the convergence rate and the influence of the functional response of the predator (parasitoid) are also provided, together with estimations of the practical cost of implementing this control strategy.