Reduced-Order Modeling Of Compartmental Metapopulation Models in Epidemiology

The theoretical modeling of an epidemic poses serious challenges due to the vast complexities of the disease-host-population system. While certain qualitative behavior can be inferred from SIR-type models, they can often be unrealistic in application owing to limiting factors such as homogeneity and geospatial isolation of the modeled population. A common remedy is to spatially decompose a population into locally homogeneous metapopulations (MPs); however, without allowing a disease to spread between MPs, the true dynamics can never be recovered, and no single MP can be modeled without simulating all of them. Furthermore, if the host mobility is highly nonlocal (e.g., as with humans), the parameter space scales as O(N²) with the number of MPs, and there is typically a dearth of data available to construct reasonable estimates for these parameters. We present a reduced-order model for a single MP to act as a framework for capturing the contributions from exterior MPs through an effective “force of infection”, which encapsulates the necessary boundary conditions to accurately model a given MP while obviating a full simulation of the system. Simulation results are compared to synthetic data, and applications to modeling the current COVID-19 pandemic are discussed.