There were 829,455 unique ED visits within the enterprise that met the inclusion criteria, with 68% of these encounters occurring prior to the start of the pandemic.
A Sankey diagram (Figure 1) was used to illustrate patient journeys, showing changes in the level of care for all patients in our study who were admitted, transferred, or died. The dominant patient journey from the ED to ward admission was followed by discharge home. An additional important pathway was ED to ICU/PCU, then ward admission, before discharge home. Inter-hospital transfers between EDs represented a small population in proportion to the whole system.
The system-wide network analysis, including all patients with an emergency department presentation during the study period, is shown in Figure 2. Node color indicates the relative importance of the node to the network using betweenness centrality, with darker nodes representing a higher betweenness centrality. Edge width indicates traffic along a connection and color the distance with darker edges representing shorter distances. The data included 1.598 million transfers with 101 nodes and 541 edges after removal of very low-frequency transfers.
Figure 2 shows extensive interconnectedness between community locations and local hospitals and with the academic center (AC). The degree connectivity between locations is visible as the background of pale-yellow lines, reflecting patients seeking emergency care in diverse places. The importance and centrality of the AC is emphasized by the high number of connections received from a vast catchment area and its high betweenness centrality.
Unsurprisingly, the most commonly used pathways are the home nodes to the nearest hospital location. However, the model also reveals a complex system structure with significant connections across farther distances when patients bypass the local facility or transfer to a distant destination. As an example, patient origin location M2 has a strong connection to its local hospital ED (MS2_ED), seen as a set of wide, dark purple lines between representing close proximity and a high volume. There is also a strong connection to AC_ED, represented by orange-yellow lines of moderate thickness. In this case, the M2 area represents the local community where the MS2 hospital is located. MS2 is a mid-sized hospital with limited specialty care and is situated near the AC, which serves as its specialty hub. Additional examples can be found with visual inspection.
Our model was found to have 101 nodes and 541 edges with a connection density of 0.054. We tested whether this system demonstrated the properties of a scale-free network, which would be resilient to random insults on nodes23. We found that the degree distribution had a heavy high degree tail but that a log-normal degree distribution with fewer very high degree nodes than would be expected within a scale-free network. The small-world parameters 𝛀24 and 𝛔25 were 0.6 and 0.3, respectively, confirming that the network behaves as a non-small world network. This places our system in contrast to scale-free small-world networks often grown organically by preferential attachment and that have specific robust characteristics26.
The average global clustering coefficient, reflecting the proportion of neighboring nodes that are also neighbors, was 0.19. This is much less than one would expect had the nodes attached randomly27. Therefore, locations that feed into a node are less likely than expected by random allocation to also feed into each other, reflecting the “hub and spoke” structure with patient origins (spokes) feeding into hospitals (hubs) and a fraction of connections transferring patients between spoke hospitals. This finding aligns with clinical observations, in which it is uncommon that a patient is transferred from a hospital that provides specialty care to one that does not or for small hospitals to transfer patients between each other.
The network is a dissociative network (overall associativity coefficient of -0.5), where nodes with high degrees are connected to nodes with lower degrees. This confirms the hub and spoke structure with patient home locations connected to their local hospital ED. However, in contrast to a connected structure, this exposes the system to higher risk if one of the hubs has reduced capacity or experiences excess demand.
Numerical determination of hubs and bottlenecks using network parameters has been described in the literature22, where hubs are the nodes with the highest degree connectivity and bottlenecks are the nodes with the highest betweenness centrality. Additionally, betweenness centrality versus degree should follow a quadratic relationship19 (Figure 3), with nodes above this curve considered bottlenecks. Both methods of determining hubs and bottlenecks agreed with few exceptions. Almost all hospital locations that are bottlenecks are also hubs (green): the EDs at all hubs (AC and RH1-3) have the highest degree and betweenness centrality. Two hospital nodes, AC_WARD and MS3_ED (red), are hubs but not bottlenecks; they are well connected but less important to the system. Several of the home locations are pure bottlenecks; in particular, O1, O2, O3 nodes (blue) encompass a larger geographical area of patients who attend a variety of hospitals. RH2_ED was determined numerically to be both a hub and bottleneck; however, the graphical analysis identified pure bottleneck characteristics.
The results of both hub/bottleneck determinations are in alignment with the clinical expectation that many patient pathways pass through an ED en route to AC_Ward and AC_ICU locations rather than non-ED locations. These nodes serve as hubs within the system without creating a significant bottleneck. O1 and O3, on the other hand, have limited connections due to proximity to their nearest facilities (RH3 and AC, respectively).
Pre- And Mid-pandemic Analysis:
Our chosen modeling timeframe encompasses pre-pandemic and mid-pandemic periods. This allows a description of the effect of changing health care provision, care-seeking behaviors, and disease incidences in our system during a critical time4.
Of the 829,455 patient encounters, ~1.1 million patient movements occurred pre-pandemic and 518,000 mid-pandemic. The two time points produced similarly structured networks. The pre-pandemic network has 111 nodes and a density of 0.18, and the mid-pandemic network has 107 nodes and a density of 0.15. Neither demonstrated small-world network characteristics, while both have a dissociative network structure (assortativity ~ -0.4). With respect to workload in AC, ED connectivity did not change significantly (pre = 152 and post = 146); however, connectivity for the ICU was reduced from 35 to 29. Most other parameters for AC did not change significantly.
We developed differential network models to represent changes in patient traffic between the two time periods (Figure 4) with the same strategy for node coloration but edge weighting and color based on the magnitude of the difference between periods. Most connections exhibited slight changes in traffic, as shown by the extensive set of thin edges. Increased patient movement was seen within the AC and from its local node M16. RH1 and RH3 saw increased patient presentations from NW2 and M11, respectively. There were increased transfers between EDSS1 and MS2, shown by the green edges connecting them (top of Figure 3), and reduced patient attendance from M2, O1 and O2.
Changes in traffic and connectivity that occurred with the onset of the pandemic are visualized by showing the percentage change in patient traffic through a node versus the percent change in degree connectivity (Figure 5). Most nodes showed little change in degree connectivity and traffic; however, there were reduced patient numbers from M13, while the CAH13 and CAH7 wards had structural changes that increased their connectivity. Figure 5 shows the increase in traffic through the relatively low volume MS3 hospital (both ward and PCU) due to accounting for proportional changes and therefore highlighting more subtle changes in traffic.