Hybrid simulation modelling of networks of heterogeneous care homes and the inter-facility spread of Covid-19 by sharing staff

Abstract

Although system dynamics [SD] and agent-based modelling [ABM] have individually served as effective tools to understand the Covid-19 dynamics, combining these methods in a hybrid simulation model can help address Covid-19 questions and study systems and settings that are difficult to study with a single approach. To examine the spread and outbreak of Covid-19 across multiple care homes via bank/agency staff and evaluate the effectiveness of interventions targeting this group, we develop an integrated hybrid simulation model combining the advantages of SD and ABM. We also demonstrate how we use several approaches adapted from both SD and ABM practices to build confidence in this model in response to the lack of systematic approaches to validate hybrid models. Our modelling results show that the risk of infection for residents in care homes using bank/agency staff was significantly higher than those not using bank/agency staff (Relative risk [RR] 2.65, 95% CI 2.57-2.72). Bank/agency staff working across several care homes had a higher risk of infection compared with permanent staff working in a single care home (RR 1.55, 95%CI 1.52-1.58). The RR of infection for residents is negatively correlated to bank/agency staff's adherence to weekly PCR testing. Within a network of heterogeneous care homes, using bank/agency staff had the most impact on care homes with lower intra-facility transmission risks, higher staff-to-resident ratio, and smaller size. Forming bubbles of care homes had no or limited impact on the spread of Covid-19. This modelling study has implications for policy makers considering developing effective interventions targeting staff working across care homes during the ongoing and future pandemics.

Fig 1. Architectural design of the integrated hybrid SD-AB model comprising three modules

Fig 2. Impact of using bank/agency staff with different compliance rates to weekly PCR testing.

A. On the cumulative number of infected residents after 90 days: Red dashed line denotes the median cumulative number of infected residents when care homes do not use bank/agency staff. Results are for 1,000 simulations in each scenario. Boxplot: middle–median; lower hinge– 25% quantile; upper hinge– 75% quantile; lower whisker = smallest observation greater than or equal to lower hinge—1.5 * IQR; upper whisker = largest observation less than or equal to upper hinge + 1.5 * IQR. B. On the risk of outbreak occurrence across care homes within 90 days. The risk of outbreak occurrence (point) is the proportion of simulations where outbreaks occur in 1,000 simulations for each scenario. Line range denotes the 95% CI of this outcome.

Fig 3. Impact of using bank/agency staff upon individual care homes with different characteristics.

The plot illustrates the relative risk [RR] of outbreaks (points) within 90 days in individual care homes using 10% bank/agency staff compared with those care homes not using bank/agency staff. A: Care homes in network B (homogeneous size & staff-to-resident ratio) with heterogeneous transmission risk drawn from a Beta distribution (shape 1 = 5, shape 2 = 266). B: Care homes in network C (homogeneous size & heterogeneous staff-to-resident ratio) with homogeneous transmission risk. C: Care homes in network D (heterogeneous size & homogeneous staff-to-resident ratio) with homogeneous transmission risk. No intervention in bank/agency staff is implemented. Line range denotes the 95% CI of the RRs. Dashed blacked vertical line denotes the RR of 1.00.

Fig 4. Impact of staffing shortage vs use of bank/agency staff on infections in residents.

The plots illustrate the distributions of cumulative number of infected residents after 90 days. A–in various levels of staff shortage. No bank/agency staff are used to cover the vacant positions. B–in various usage levels of bank/agency staff. Bank/agency staff have 80% compliance to weekly PCR testing (α = 0.5). Boxplot: middle–median; lower hinge– 25% quantile; upper hinge– 75% quantile; lower whisker = smallest observation greater than or equal to lower hinge—1.5 * IQR; upper whisker = largest observation less than or equal to upper hinge + 1.5 * IQR.

Fig 5. Impact of staffing shortage verse use of bank/agency staff on the risk of outbreak.

The plots illustrate the risk of outbreak occurrence across care homes within 90 days. A–in various levels of staff shortage. No bank/agency staff is used to cover the vacant positions. B–in various usage levels of bank/agency staff. Bank/agency staff have 80% compliance to weekly PCR testing (α = 0.5). The risk of outbreak occurrence (point) is the proportion of simulations where outbreaks occur in 1,000 simulations for each scenario. Line range denotes the 95% CI of this outcome.