GLOBAL ERADICATION FOR SPATIALLY STRUCTURED POPULATIONS BY REGIONAL CONTROL

This paper concerns problems for the eradication of a population by acting on a subregion omega. The dynamics is described by a general reaction-diffusion system, including one or more populations, subject to a vital dynamics with either local logistic or nonlocal logistic terms. For the one population case, a necessary condition and a sufficient condition for eradicability (zero-stabilizability) are obtained, in terms of the sign of the principal eigenvalue of a suitable elliptic operator acting on the domain Omega\(omega) over bar : A feedback harvesting-like control with a large constant harvesting rate realizes eradication of the population. The problem of eradication is then reformulated in a more convenient way, by taking into account the total cost of the damages produced by a pest population and the costs related to the choice of the relevant subregion, and approximated by a regional optimal control problem with a finite horizon. A conceptual iterative algorithm is formulated for the simulation of the proposed optimal control problem. Numerical tests are given to illustrate the effectiveness of the results. Relevant regional control problems for two populations reaction-diffusion models, such as prey-predator system, and an SIR epidemic system with spatial structure and local/nonlocal force of infection, have been analyzed too.