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

TL;DR

This work presents a hybrid ABM-PDE framework that couples a PDE-based seven-state compartmental model for Berlin with an ABM driven by mobile-phone trajectories for Brandenburg, enabling efficient, large-scale simulation of infectious disease spread across heterogeneous regions. The boundary exchanges preserve mass between domains, with agents entering PDE domain represented as densities and PDE densities spawning ABM agents to maintain continuity. Parameter identification combines a calibrated PDE infection rate informed by activity changes and ABM parameters borrowed from prior work (e.g., EpiSim), with coarse grid-search fitting on real mobility and infection data. Numerical results show substantial reductions in the required number of runs and simulation time while achieving lower or comparable mean absolute errors relative to full ABM, for both 25% and 100% population scenarios, and demonstrate robustness under extreme coupling tests. The framework offers a practical path toward real-time, large-scale epidemiological assessments in regions with pronounced urban-rural contrasts and commuting flows, with potential extensions to ABM-PDE-ODE coupling.

Abstract

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.

Figures (20)

• Figure 1: Structure of the SEIYHCR model with seven health states and ten transition rules, capturing disease progression from Susceptble to Recovered via intermediate states.
• Figure 2: Activity participation in % for activities at home and not at home including weekends.
• Figure 3: Modeling domain of PDE contribution (\ref{['eq:PDE-model']}) of hybrid model.
• Figure 4: Cumulative absolute mean error of 100 runs using a 25% population sample. Red line is mean of all cumulative runs.
• Figure 5: Cumulative mean running times of 10 runs using a 25% population sample. Red line is mean of all cumulative runs.