Verifying Infectious Disease Scenario Planning for Geographically Diverse Populations

In the face of the COVID-19 pandemic, the literature saw a spike in publications for epidemic models, and a renewed interest in capturing contact networks and geographic movement of populations. There remains a general lack of consensus in the modeling community around best practices for spatiotemporal epi-modeling, specifically as it pertains to the infection rate formulation and the underlying contact or mixing model.

In this work, we mathematically verify several common modeling assumptions in the literature, to prove when certain choices can provide consistent results across different geographic resolutions, population densities and patterns, and mixing assumptions. The most common infection rate formulation, a computationally low cost per capita infection rate assumption, fails the consistency tests for heterogeneous populations and non-symmetric mixing assumptions. The largest numerical errors occur in the limit of lowest symmetry, whether as sparse geography or preferential travel to highly-populated locations. Future modeling efforts in spatiotemporal disease modeling should be wary of this limitation, particularly when working with more heterogenous or less dense populations.

Our results provide guidance for testing that a model preserves desirable properties even when model inputs mask potential problems due to symmetry or homogeneity. We also provide a recipe for performing this type of validation with the objective of strengthening decision support tools.

Highlights

• Define common modeling options from the literature for spatiotemporal epidemic models

• Verify common modeling assumptions are consistent for varying population densities and patterns, resolutions, and underlying mixing or contact assumptions

• Provide simulation examples of model misspecification and the resulting implications on scenario planning