Global Density Analysis for an Off-Lattice Agent-Based Model

TL;DR

This paper introduces a general method to analyze off-lattice agent-based models by defining a Global Recurrence Rule, enabling efficient estimation of long-term behavior and steady states, demonstrated on an epidemiological model.

Contribution

It develops a precise mathematical framework for off-lattice AB models with interaction neighborhoods, allowing accurate long-term predictions without extensive simulations.

Findings

The GRR accurately predicts long-term behavior.

The framework applies to various models beyond epidemiology.

Steady states can be determined analytically.

Abstract

Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational model is often counterbalanced by the difficulty of performing rigorous analysis to determine emergent behaviors. In addition, without precise definitions of cell interactions, calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially thousands of simulations. Through developing a precise definition of an off-lattice CA or AB model with a specified interaction neighborhood, we develop a general method to determine a Global Recurrence Rule (GRR). This allows estimates of the state densities in time, which can be easily calculated for a range of parameters in the model. The utility of this framework is tested on an Epidemiological Cellular Automata (E-CA) model where agents or cells correspond to people that are in the susceptible, infected, or recovered states. The interaction neighborhoods of cells are determined in a mathematical formulation that allows the GRR to accurately predict the long term behavior and steady states. The modeling framework outlined will be generally applicable to many areas and can be easily extended.