SPARSEMODr: Rapidly simulate spatially explicit and stochastic models of COVID-19 and other infectious diseases.

Building realistically complex models of infectious disease transmission that are relevant for informing public health is conceptually challenging and requires knowledge of coding architecture that can implement key modeling conventions. For example, many of the models built to understand COVID-19 dynamics have included stochasticity, transmission dynamics that change throughout the epidemic due to changes in host behavior or public health interventions, and spatial structures that account for important spatio-temporal heterogeneities. Here we introduce an R package, SPARSEMODr, that allows users to simulate disease models that are stochastic and spatially explicit, including a model for COVID-19 that was useful in the early phases of the epidemic. SPARSEMOD stands for SPAtial Resolution-SEnsitive Models of Outbreak Dynamics, and our goal is to demonstrate particular conventions for rapidly simulating the dynamics of more complex, spatial models of infectious disease. In this report, we outline the features and workflows of our software package that allow for user-customized simulations. We believe the example models provided in our package will be useful in educational settings, as the coding conventions are adaptable, and will help new modelers to better understand important assumptions that were built into sophisticated COVID-19 models.

A sliding window approach to optimize the time-varying parameters of a spatially-explicit and stochastic model of COVID-19.

The implementation of non-pharmaceutical public health interventions can have simultaneous impacts on pathogen transmission rates as well as host mobility rates. For instance, with SARS-CoV-2, masking can influence host-to-host transmission, while stay-at-home orders can influence mobility. Importantly, variations in transmission rates and mobility patterns can influence pathogen-induced hospitalization rates. This poses a significant challenge for the use of mathematical models of disease dynamics in forecasting the spread of a pathogen; to create accurate forecasts in spatial models of disease spread, we must simultaneously account for time-varying rates of transmission and host movement. In this study, we develop a statistical model-fitting algorithm to estimate dynamic rates of SARS-CoV-2 transmission and host movement from geo-referenced hospitalization data. Using simulated data sets, we then test whether our method can accurately estimate these time-varying rates simultaneously, and how this accuracy is influenced by the spatial population structure. Our model-fitting method relies on a highly parallelized process of grid search and a sliding window technique that allows us to estimate time-varying transmission rates with high accuracy and precision, as well as movement rates with somewhat lower precision. Estimated parameters also had lower precision in more rural data sets, due to lower hospitalization rates (i.e., these areas are less data-rich). This model-fitting routine could easily be generalized to any stochastic, spatially-explicit modeling framework, offering a flexible and efficient method to estimate time-varying parameters from geo-referenced data sets.