Construction of a demand and capacity model for intensive care and hospital ward beds, and mortality from COVID-19
Authors: McDonald Stuart , Martin Chris , Bale Steve , Luteijn Michiel , Sarkar Rahul 
Published: January 2021

AbstractBackgroundThis paper describes the construction of a model used to estimate the number of excess deaths that could be expected as a direct consequence of a lack of hospital bed and intensive care unit (ICU) capacity.MethodsA series of compartmental models was used to estimate the number of deaths under different combinations of care required (ICU or ward), and care received (ICU, ward or no care) in England up to the end of April 2021. Model parameters were sourced from publicly available government information, organisations collating COVID-19 data and calculations using existing parameters. A compartmental sub-model was used to estimate the mortality scalars that represent the increase in mortality that would be expected from a lack of provision of an ICU or general ward bed when one is required. Three illustrative scenarios for admissions numbers, ‘Optimistic’, ‘Middling’ and ‘Pessimistic’, are described showing how the model can be used to estimate mortality rates under different scenarios of capacity.ResultsThe key output of our collaboration was the model itself rather than the results of any of the scenarios. The model allows a user to understand the excess mortality impact arising as a direct consequence of capacity being breached under various scenarios or forecasts of hospital admissions. The scenarios described in this paper are illustrative and are not forecasts.There were no excess deaths from a lack of capacity in any of the ‘Optimistic’ scenario applications in sensitivity analysis.Several of the ‘Middling’ scenario applications under sensitivity testing resulted in excess deaths directly attributable to a lack of capacity. Most excess deaths arose when we modelled a 20% reduction compared to best estimate ICU capacity. This led to 597 deaths (0.7% increase).All the ‘Pessimistic’ scenario applications under sensitivity analysis had excess deaths. These ranged from 49,219 (19.4% increase) when we modelled a 20% increase in ward bed availability over the best-estimate, to 103,845 (40.9% increase) when we modelled a 20% shortfall in ward bed availability below the best-estimate. The emergence of a new, more transmissible variant (VOC 202012/01) increases the likelihood of real world outcomes at, or beyond, those modelled in our ‘Pessimistic’ scenario.The results can be explained by considering how capacity evolves in each of the scenarios. In the Middling scenario, whilst ICU capacity may be approached and even possibly breached, there remains sufficient ward capacity to take lives who need either ward or ICU support, keeping excess deaths relatively low. However, the Pessimistic scenario sees ward capacity breached, and in many scenarios for a period of several weeks, resulting in much higher mortality in those lives who require care but do not receive it.ConclusionsNo excess deaths from breaching capacity would be expected under the unadjusted ‘Optimistic’ assumptions of demand. The ‘Middling’ scenario could result in some excess deaths from breaching capacity, though these would be small (0.7% increase) relative to the total number of deaths in that scenario. The ‘Pessimistic’ scenario would certainly result in significant excess deaths from breaching capacity. Our sensitivity analysis indicated a range between 49,219 (19.4% increase) and 103,845 (40.9% increase) excess deaths.Without the new variant, exceeding capacity for hospital and ICU beds did not appear to be the most likely outcome but given the new variant it now appears more plausible and, if so, would result in a substantial increase in the number of deaths from COVID-19.