AGRO-ECOLOGICAL CONTROL OF A PEST-HOST SYSTEM: PREVENTING SPREADING

We consider an agro-ecologically motivated coupling between a prey-predator system and a vector-borne epidemic system. The coupled system contains one ODE, two reaction-diffusion PDEs, and one reaction-diffusion-advection PDE; it has no complete variational or monotonic structure and coefficients are spatially heterogeneous. We study the long-time behavior of solutions of the Cauchy-Neumann problem, which turns out to be largely decided by a linear stability criterion but still involves nonlinear subtleties. Then we consider an optimal control problem. Although it remains elusive analytically, we show numerically the variety of outcomes and the strong impact of the initial conditions.

Automated summary

This passage discusses an agro-ecologically motivated coupling model of a prey-predator system and a vector-borne epidemic system. The model consists of one ODE and three reaction-diffusion PDEs, with spatially heterogeneous coefficients and no complete variational or monotonic structure. The long-term behavior of solutions of the Cauchy-Neumann problem is studied, which is largely determined by a linear stability criterion but still involves nonlinear subtleties. An optimal control problem is then considered, and although it remains analytically elusive, numerical simulations show a variety of outcomes and the strong impact of initial conditions.