arXiv subjects

Kristina Kehrer

Publications and source records attributed to Kristina Kehrer.

3 recordsLinked to original sources

arXiv2026

Mobility-Informed Coupling of ABM, PDE, and ODE Models for Pandemic Simulation in Germany

Simulating epidemic spread across an entire country requires balancing fine-grained realism with computational feasibility. We address this trade-off with a multiscale, hybrid modeling framework for simulating the spread of COVID-19 across Germany. The spatial domain is split into regions, each represented either by a high-resolution agent-based model (ABM) incorporating mobility data from mobile phones or by a faster, less detailed model based on partial (PDEs) or ordinary differential equations (ODEs). Data-driven jump processes model mobility between regions, enabling individuals to be transferred between model domains. Building on earlier studies on pairwise coupling strategies, we develop a unified framework that combines all three model classes within a single simulation environment. To demonstrate the framework's utility, we systematically compare ABM, PDE, and ODE representations of Berlin embedded in a nationwide simulation of Germany, investigate regional travel restrictions, and evaluate the Zero-COVID and No-COVID strategies. The results indicate that model resolution can be reduced in sufficiently homogeneous regions without substantially altering epidemic dynamics. Further, they reveal that mobility restrictions can lead to non-intuitive outcomes, including cases in which regional border closures increase infection numbers both locally and nationally. These effects are observed even between non-adjacent regions, illustrating how emergent, system-wide dynamics arise from local mobility restrictions. We quantify computational performance in terms of runtime savings and validate the framework against real-world infection data. The results show that the hybrid framework substantially reduces computational cost without sacrificing predictive accuracy, offering a practical tool for evaluating regional mobility restrictions and public health interventions at national scale.

physics.soc-ph↗

arXiv2026

A Hybrid ABM-PDE Framework for Real-World Infectious Disease Simulations

This paper presents a hybrid modeling approach that couples an Agent-Based Model (ABM) with a partial differential equation (PDE) model in an epidemic setting to simulate the spatial spread of infectious diseases using a compartmental structure with seven health states. The goal is to reduce the computational complexity of a full-ABM by introducing a coupled ABM-PDE model that offers significantly faster simulations while maintaining comparable accuracy. Our results demonstrate that the hybrid model not only reduces the overall simulation runtime (defined as the number of runs required for stable results multiplied by the duration of a single run) but also achieves smaller errors across both 25% and 100% population samples. The coupling mechanism ensures consistency at the model interface: agents crossing from the ABM into the PDE domain are removed and represented as density contributions, while surplus density in the PDE domain is used to generate agents with plausible trajectories derived from mobile phone data. We evaluate the hybrid model using real-world mobility and infection data for the Berlin-Brandenburg region in Germany, showing that it captures the core epidemiological dynamics while enabling efficient large-scale simulations. These results demonstrate that the proposed ABM-PDE framework provides a robust and computationally efficient alternative to full-scale agent-based simulations, making it suitable for realistic epidemic modeling and scenario analysis.

cs.MA↗

arXiv2024

Hybrid PDE-ODE Models for Efficient Simulation of Infection Spread in Epidemiology

This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of PDEs and the computational efficiency of ODEs, the model enables rapid evaluation of public health interventions. Applied to synthetic environments and real-world scenarios in Lombardy, Italy, and Berlin, Germany, the model highlights how interactions between PDE and ODE regions affect infection dynamics, especially in high-density areas. Key findings reveal that the placement of model boundaries in densely populated regions can lead to inaccuracies in infection spread, suggesting that boundaries should be positioned in areas of lower population density to better reflect transmission dynamics. Additionally, regions with low population density hinder infection flow, indicating a need for incorporating, e.g., jumps in the model to enhance its predictive capabilities. Results indicate that the hybrid model achieves a balance between computational speed and accuracy, making it a valuable tool for policymakers in real-time decision-making and scenario analysis in epidemiology and potentially in other fields requiring similar modeling approaches.

math.DS↗