Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.

基于代理的模型 (ABM) 是对时空人口动态进行建模的有用工具，模型描述中可以包含许多细节。尽管它们的计算成本非常高，并且对于随机 ABM，需要大量单独的模拟来对感兴趣的数量进行采样。特别是，大量代理人使抽样变得不可行。将模型简化为集合种群模型可显着提高计算效率，同时保留重要的动力学特性。基于对时空 ABM 的精确数学描述，我们提出了两种不同的集合种群方法（随机和分段确定性），并讨论了该框架内不同模型之间的近似步骤。尤其，我们展示了随机集合种群模型是如何从基础 ABM 的伽辽金投影到有限维模拟空间上产生的。最后，我们利用我们的建模框架为 COVID-19 的传播提供了一个概念模型，该模型可以扩展到现实世界的场景。