Repository: Freie Universität Berlin, Math Department

Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading

Winkelmann, Stefanie and Zonker, J. and Schütte, Christof and Djurdjevac Conrad, Natasa (2021) Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading. Mathematical Biosciences, 336 .

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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.

Item Type:Article
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2972
Deposited By: Monika Drueck
Deposited On:02 May 2023 10:54
Last Modified:02 May 2023 10:54

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