"Systematic reduction of spatio-temporal population dynamics and application to epidemic spreading"Winkelmann, StefanieAgent-based models (ABMs) are valuable for simulating spatio-temporal population dynamics, allowing for detailed descriptions. However, they entail high computational costs, particularly for large populations and for stochastic dynamics requiring numerous individual simulations. Reduction to metapopulation models significantly enhances computational efficiency while retaining essential dynamic properties. In this talk, we introduce two metapopulation models (stochastic and piecewise deterministic) derived from precise mathematical descriptions of spatio-temporal ABMs. We discuss the approximation steps between these models, highlighting the derivation of the stochastic metapopulation model through Galerkin projection onto a finite-dimensional ansatz space. Finally, we apply our modeling framework to provide a conceptual model for epidemic spreading that can be scaled to real-world scenarios. |
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