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

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

Problem Statement
Accurate simulation of infectious disease dynamics in highly interconnected nations like Germany requires balancing high-resolution spatial and behavioral detail with computational scalability. Purely agent-based models (ABMs) offer fine-grained representation of individual mobility and interactions but become computationally prohibitive at the national scale. Conversely, aggregated models like Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs) are computationally efficient but lack the spatial and stochastic resolution necessary to capture local heterogeneity and complex mobility patterns. The challenge lies in developing a unified framework that integrates these distinct modeling paradigms to simulate nationwide epidemic spread while preserving local accuracy where it matters most.

Methodology
The authors present a hybrid modeling framework that couples three distinct model classes—Agent-Based Models (ABM), Partial Differential Equations (PDE), and Ordinary Differential Equations (ODE)—within a single simulation environment. The framework is built upon the C++ implementation of the EpiSim ABM, utilizing high-resolution mobile phone data to reconstruct individual trajectories and daily routines.

• Model Components:

  • ABM: Represents a 25% sample of the German population. Agents move between facilities (homes, workplaces, schools) based on mobile phone-derived trajectories. Infection transmission occurs only when susceptible and infectious agents co-locate within the same facility category.
  • PDE: Used for regions where spatial heterogeneity is relevant but full agent-level simulation is too costly. The PDE system is derived from a motion-based ABM approximation, utilizing a "landscape" function $V(x)$ derived from mobile phone data to drive diffusion and advection terms. The infection term is localized to account for the coarse spatial mesh.
  • ODE: Used for regions assumed to be homogeneously mixed. This is a further reduction of the PDE system, aggregating densities into compartment counts for the entire federal state.

• Coupling Mechanism:
  The framework employs data-driven "jump processes" to transfer individuals between model domains at each time step.

  • ABM to Non-ABM: Agents leaving an ABM domain are either added as discrete counts to an ODE domain or converted into spatial density contributions for a PDE domain.
  • Non-ABM to ABM: Individuals from PDE/ODE domains are mapped back to the ABM as new agents.
  • Non-ABM to Non-ABM: Transfers between PDE and ODE domains are handled by distributing individuals according to current compartment fractions, ensuring mass conservation.
  • Mobility Logic: To prevent premature infection transmission in simplified models, agents traveling from an ABM state to a non-ABM state remain in the ABM domain until they reach their destination. Conversely, agents entering an ABM domain are converted to agents as early as possible.

• Interventions:
  The model incorporates activity reductions (e.g., lockdowns) by removing events in the ABM and scaling infection rates in PDE/ODE domains. It also simulates border closures by suppressing inter-state transfers and complex intervention strategies like "Zero-COVID" and "No-COVID," which trigger restrictions based on 7-day or 14-day incidence thresholds.

Key Contributions

1. Unified Hybrid Framework: The paper develops a novel coupling strategy that unifies ABM, PDE, and ODE models, allowing different German federal states to be simulated at varying levels of resolution within a single run.
2. Data-Driven Mobility Integration: The framework integrates real-world mobile phone data to drive both the agent trajectories in the ABM and the landscape functions in the PDE models, ensuring that inter-regional mobility is grounded in empirical data rather than theoretical assumptions.
3. Scalable National Simulation: By simulating a 25% population sample and assigning model types based on computational constraints and population size, the authors demonstrate the feasibility of running nationwide simulations that retain local detail (e.g., in Berlin) while using aggregated models for other regions.
4. Policy Evaluation Tool: The framework is applied to evaluate specific public health interventions, including complete border closures and the comparative efficacy of Zero-COVID versus No-COVID strategies.

Results

• Accuracy vs. Efficiency: In experiments where Berlin was modeled as an ABM, PDE, or ODE, the ABM representation yielded the lowest error against real-world infection data (RKI data), followed by ODE and then PDE. However, the ABM configuration was the slowest, while the ODE configuration was the fastest. The hybrid approach offers a trade-off, reducing runtime significantly compared to a full ABM simulation while maintaining better accuracy than a purely aggregated model.
• Border Closures: Simulating complete border closures for Berlin reduced symptomatic cases in Berlin but had non-linear effects on other states; some states (e.g., Mecklenburg-Vorpommern, Saxony) saw an increase in cases, highlighting that mobility restrictions can produce counter-intuitive outcomes depending on commuting patterns.
• Intervention Strategies: The Zero-COVID strategy (restrictions triggered by 7-day incidence > 1) was found to be substantially more effective at reducing symptomatic cases than the No-COVID strategy (triggered by mystery cases over 14 days) and more effective than total border closures. However, the study notes that the No-COVID strategy performed worse than total border closures when North Rhine-Westphalia was excluded from the aggregate metrics.
• Computational Performance: The authors estimate that a full-year simulation of Germany using only ABMs would take approximately 497 days (without parallelization), whereas the hybrid model reduces this to roughly 72 days for a sufficient number of runs to achieve statistical accuracy.

Significance and Claims
The paper claims that this hybrid framework provides a practical tool for evidence-based evaluation of public health interventions at the national scale. It demonstrates that coupling different modeling resolutions allows researchers to analyze the interplay between mobility, regional coupling, and containment measures without incurring the prohibitive computational costs of a full agent-based simulation. The authors emphasize that while the framework enables efficient and accurate simulation of infection dynamics across densely connected regions, the results are proof-of-concept. They note that the current parameter choices are sufficient to demonstrate the framework's utility but that further optimization could reduce errors. The study concludes that such hybrid models are essential for exploring epidemic dynamics in heterogeneous regions where interregional mobility and policy interventions play critical roles, offering a scalable alternative to purely stochastic or purely deterministic approaches.