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

TL;DR

This paper presents a hybrid PDE-ODE model that combines spatial detail and computational efficiency to simulate infectious disease spread, aiding rapid public health decision-making.

Contribution

The novel hybrid PDE-ODE approach improves simulation speed and accuracy for epidemiological modeling across geographic regions.

Findings

Placement of boundaries affects infection accuracy.

Low-density regions slow infection flow.

Model balances speed and precision effectively.

Abstract

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.