期刊
MATHEMATICAL BIOSCIENCES
卷 336, 期 -, 页码 -出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.mbs.2021.108619
关键词
Agent-based model; Metapopulation model; Spatio-temporal master equation; Population dynamics; Piecewise-deterministic Markov process; Epidemic spreading; Galerkin projection
资金
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [CRC 1114/2]
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy The Berlin Mathematics Research Center MATH+ [EXC-2046/1, 390685689]
Agent-based models are useful for modeling spatio-temporal population dynamics but come with high computational costs. Model reduction to a metapopulation model can improve efficiency while preserving key dynamical properties. The stochastic metapopulation model can be seen as a simplified projection of the underlying ABM through mathematical description.
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.
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