Control of a consumer-resource agent-based model using partial differential equation approximation

Agent-based models (ABMs) are increasing in popularity as tools to simulate and explore many biological systems. Successes in simulation lead to deeper investigations, from designing systems to optimizing performance. The typically stochastic, rule-based structure of ABMs, however, does not lend itself to analytic and numerical techniques of optimization the way traditional dynamical systems models do. The goal of this work is to illustrate a technique for approximating ABMs with a partial differential equation (PDE) system to design some management strategies on the ABM. We propose a surrogate modeling approach, using differential equations that admit direct means of determining optimal controls, with a particular focus on environmental heterogeneity in the ABM. We implement this program with both PDE and ordinary differential equation (ODE) approximations on the well-known rabbits and grass ABM, in which a pest population consumes a resource. The control problem addressed is the reduction of this pest population through an optimal control formulation. After fitting the ODE and PDE models to ABM simulation data in the absence of control, we compute optimal controls using the ODE and PDE models, which we them apply to the ABM. The results show promise for approximating ABMs with differential equations in this context.