Optimal control of harvesting in a stochastic metapopulation model

Abstract

SUMMARYWe consider a metapopulation model for a single species inhabiting two bounded contiguous regions where movement of the population across the shared boundary is allowed. The population in one of the bounded regions can be harvested. We introduce stochastic growth rates for the two populations in a system of ordinary differential equations that model the population dynamics in these two regions. We derive the resulting stochastic control problem with harvesting in the one region as the control. The existence of an optimal control is established by solving an associated quasi-linear-quadratic optimal control problem. We present numerical simulations to illustrate several scenarios.