Nataša Djurdjevac Conrad, Martin Weiser, Sarah Wolf, Edda Klipp
Jan-Hendrik Niemann (FU Berlin), Björn Goldenbogen (HU Berlin)
01.01.2022 – 31.12.2023
FU Berlin, HU Berlin
Epidemiological agent-based models (ABMs) such as the GEospatially Referenced Demographic ABM (GERDA)  can simulate and forecast infection spreading in much detail and, if parametrized correctly, with high accuracy. They incur, however, a huge computational effort and a large set of uncertain parameters. We develop multilevel representations of ABMs using network-based coarsening and model identification techniques in order to improve the understanding of pattern formation and to accelerate parameter identification and policy optimization.
Efficient multilevel optimization requires suitable coarse models. Obvious candidates such as the established SIR models are often not rich enough to reflect spatial or subpopulation effects and related parameters such as in GERDA. We find coarse models providing a good trade-off between complexity, approximation quality, and extrapolation power via network-based coarsening and model identification techniques, see, e.g., [2, 3]. Their effectivity is evaluated in multilevel optimization and compared with available coarse-grained and SIR-type models.
Another essential step towards nonlinear multilevel parameter identification and policy optimization is the efficient computation of derivatives with respect to model parameters. Since straightforward numerical differentiation of (stochastic and discontinuous) ABMs is infeasibly expensive due to their computational complexity and variance, we study the combined use of hierarchical Monte Carlo methods and adjoint concepts for efficient gradient computation. Figure 1 shows (a) an exemplary optimal control policy in terms of home office and home schooling computed for a coarse SIR model fitted to GERDA and its impact on the infection numbers, see (b) and (c).
In a complementary approach we are aiming for a coarse grained ABM that reflects the key characteristics of the original model but is reduced with respect to time steps or agent number. Based on the temporal interaction and infection networks spanned by the original ABM, we analyze the involvement and degrees of connection of population subgroups and search for dominant infection patterns. Further we develop methods for compression of the undirected interaction graphs and the directed infection graphs retaining the relevant information, to eventually establish algorithms to coarse grain GERDA .
Exemplary optimal policy computed for a coarse SIR model fitted to GERDA and its impact on the infection numbers, see (b) and (c). The policy is to apply different levels of home office and home schooling, where 0 means no home office or home schooling is applied and 1 means the opposite, i.e., neither presence at work nor at school.
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