How much do superspreaders matter? Epidemic dynamics in inhomogeneous populations (preprint)

A variant of the SIR model for an inhomogeneous population is introduced in order to account for the effect of variability in susceptibility and infectiousness across a population. An initial formulation of this dynamics leads to infinitely many differential equations. Our model, however, can be reduced to a single first-order one-dimensional differential equation. Using this approach, we provide quantitative solutions for different distributions. In particular, we use GPS data from ~107 cellphones to determine an empirical distribution of the number of individual contacts and use this to infer a possible distribution of susceptibility and infectivity. We quantify the effect of superspreaders on the early growth rate R0 of the infection and on the final epidemic size, the total number of people who are ever infected. We discuss the features of the distribution that contribute most to the dynamics of the infection.

Mobility network modeling explains higher SARS-CoV-2 infection rates among disadvantaged groups and informs reopening strategies (preprint)

Fine-grained epidemiological modeling of the spread of SARS-CoV-2 -- capturing who is infected at which locations -- can aid the development of policy responses that account for heterogeneous risks of different locations as well as the disparities in infections among different demographic groups. Here, we develop a metapopulation SEIR disease model that uses dynamic mobility networks, derived from US cell phone data, to capture the hourly movements of millions of people from local neighborhoods (census block groups, or CBGs) to points of interest (POIs) such as restaurants, grocery stores, or religious establishments. We simulate the spread of SARS-CoV-2 from March 1-May 2, 2020 among a population of 105 million people in 10 of the largest US metropolitan statistical areas. We show that by integrating these mobility networks, which connect 60k CBGs to 565k POIs with a total of 5.4 billion hourly edges, even a relatively simple epidemiological model can accurately capture the case trajectory despite dramatic changes in population behavior due to the virus. Furthermore, by modeling detailed information about each POI, like visitor density and visit length, we can estimate the impacts of fine-grained reopening plans: we predict that a small minority of "superspreader" POIs account for a large majority of infections, that reopening some POI categories (like full-service restaurants) poses especially large risks, and that strategies restricting maximum occupancy at each POI are more effective than uniformly reducing mobility. Our models also predict higher infection rates among disadvantaged racial and socioeconomic groups solely from differences in mobility: disadvantaged groups have not been able to reduce mobility as sharply, and the POIs they visit (even within the same category) tend to be smaller, more crowded, and therefore more dangerous. By modeling who is infected at which locations, our model supports fine-grained analyses that can inform more effective and equitable policy responses to SARS-CoV-2.