Lessons from movement ecology for the return to work: Modeling contacts and the spread of COVID-19

Human behavior (movement, social contacts) plays a central role in the spread of pathogens like SARS-CoV-2. The rapid spread of SARS-CoV-2 was driven by global human movement, and initial lockdown measures aimed to localize movement and contact in order to slow spread. Thus, movement and contact patterns need to be explicitly considered when making reopening decisions, especially regarding return to work. Here, as a case study, we consider the initial stages of resuming research at a large research university, using approaches from movement ecology and contact network epidemiology. First, we develop a dynamical pathogen model describing movement between home and work; we show that limiting social contact, via reduced people or reduced time in the workplace are fairly equivalent strategies to slow pathogen spread. Second, we develop a model based on spatial contact patterns within a specific office and lab building on campus; we show that restricting on-campus activities to labs (rather than labs and offices) could dramatically alter (modularize) contact network structure and thus, potentially reduce pathogen spread by providing a workplace mechanism to reduce contact. Here we argue that explicitly accounting for human movement and contact behavior in the workplace can provide additional strategies to slow pathogen spread that can be used in conjunction with ongoing public health efforts.


September 2, 2020
To evaluate the sensitivity of the network model results in the main text, here we perform further disease simulations on random graphs that are structurally similar to the empirical networks. First, we performed configuration model randomizations of each of the empirical networks. A configuration model preserves the exact degree distribution of the network, while allowing other structures to vary freely. This approach allows for the generation of "similar" networks upon which we can simulate disease dynamics and compare outcomes to those seen in the empirical networks. This model provided a fairly good fit to the combined lab and office-space network used in the main text, but fit the shared lab-space network poorly due to its highly fragmented structure. Thus, we additionally generated random graphs that kept the approximate number and size of isolated components as the shared lab-space network.
We provide additional details and figures for each of these cases below. Code to replicate these analyses can be found at https://github.com/whit1951/EEBCovid.

Configuration model
To generate the random graphs with degree sequences matching those of the empirical networks, we utilized the sample_degseq function in the igraph [Csardi and Nepusz, 2006] package for R (Version 4.0.2; R Core Team, 2020). We generated 200 random graphs for each of the two empirical networks from the main text. For each random graph, we simulated 50 epidemics as detailed in the main text, recording the epidemic peak (the maximum number of concurrently infectious individuals), the final epidemic size (the total number of individuals infected over the course of the epidemic), and the time to epidemic peak (the number of days before the epidemic peak is reached) for each simulation.
For the combined lab-and office-space network, this produced networks with similar, but in general less fragmented structure (figs. S8 and S9), which yielded similar, though slightly larger, disease dynamics (i.e. higher peak, more total infected, and longer times to epidemic peak; fig. S10). This discrepancy is likely a consequence of the reduced fragmentation in randomized networks compared to the empirical networks.

Isolated block model
As noted above, the configuration model does not accurately capture fragmented networks, instead producing networks with one large connected component and several very small components. This is particularly noticeable when comparing the random graphs to the shared lab-space network. To compensate for this, we ran additional simulations that generated a network of approximately the same size (i.e. number of individuals) and distribution of isolated cluster sizes as the network of shared lab-space. Note that we did not, however, recreate the few cases where two lab-spaces are linked by a single individual. Instead, in these simulated networks all individuals within a lab are connected to all other individuals in the same lab. Put another way, in contrast to the empirical network, in these simulated networks the shortest path between any two individuals (assuming such a path exists) is always one. We did this by generating a number of small, fully connected graphs, whose size was randomly drawn from the distribution of component sizes in the original lab-space network, and then merging all of these components into a single network for further analysis.
These synthetic networks better captured the structure of the shared lab-space network (fig. S11, and were able to recapitulate the disease dynamics seen on the empirical labspace network ( fig. S12).
Additional packages used in these simulations include tidyverse [Wickham et al., 2019], tidygraph [Pedersen, 2020], and janitor [Firke, 2020].  fig. S8 above, but including results from a block-model randomization of the two shared lab-space network. Figure S12: As fig. 7 in the main text and fig. S10 above, but including results from a block-model randomization of the shared lab-space empirical network.