The False Economy of Seeking to Eliminate Delayed Transfers of Care: Some Lessons from Queueing Theory.

BACKGROUND: It is a stated ambition of many healthcare systems to eliminate delayed transfers of care (DTOCs) between acute and step-down community services. OBJECTIVE: This study aims to demonstrate how, counter to intuition, pursual of such a policy is likely to be uneconomical, as it would require large amounts of community capacity to accommodate even the rarest of demand peaks, leaving much capacity unused for much of the time. METHODS: Some standard results from queueing theory-a mathematical discipline for considering the dynamics of queues and queueing systems-are used to provide a model of patient flow from the acute to community setting. While queueing models have a track record of application in healthcare, they have not before been used to address this question. RESULTS: Results show that 'eliminating' DTOCs is a false economy: the additional community costs required are greater than the possible acute cost saving. While a substantial proportion of DTOCs can be attributed to inefficient use of resources, the remainder can be considered economically essential to ensuring cost-efficient service operation. For England's National Health Service (NHS), our modelling estimates annual cost savings of £117m if DTOCs are reduced to the 12% of current levels that can be regarded as economically essential. CONCLUSION: This study discourages the use of 'zero DTOC' targets and instead supports an assessment based on the specific characteristics of the healthcare system considered.

Optimising the balance of acute and intermediate care capacity for the complex discharge pathway: Computer modelling study during COVID-19 recovery in England.

OBJECTIVES: While there has been significant research on the pressures facing acute hospitals during the COVID-19 pandemic, there has been less interest in downstream community services which have also been challenged in meeting demand. This study aimed to estimate the theoretical cost-optimal capacity requirement for 'step down' intermediate care services within a major healthcare system in England, at a time when considerable uncertainty remained regarding vaccination uptake and the easing of societal restrictions. METHODS: Demand for intermediate care was projected using an epidemiological model (for COVID-19 demand) and regressing upon public mobility (for non-COVID-19 demand). These were inputted to a computer simulation model of patient flow from acute discharge readiness to bedded and home-based Discharge to Assess (D2A) intermediate care services. Cost-optimal capacity was defined as that which yielded the lowest total cost of intermediate care provision and corresponding acute discharge delays. RESULTS: Increased intermediate care capacity is likely to bring about lower system-level costs, with the additional D2A investment more than offset by substantial reductions in costly acute discharge delays (leading also to improved patient outcome and experience). Results suggest that completely eliminating acute 'bed blocking' is unlikely economical (requiring large amounts of downstream capacity), and that health systems should instead target an appropriate tolerance based upon the specific characteristics of the pathway. CONCLUSIONS: Computer modelling can be a valuable asset for determining optimal capacity allocation along the complex care pathway. With results supporting a Business Case for increased downstream capacity, this study demonstrates how modelling can be applied in practice and provides a blueprint for use alongside the freely-available model code.

Estimates of regional infectivity of COVID-19 in the United Kingdom following imposition of social distancing measures.

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) reproduction number has become an essential parameter for monitoring disease transmission across settings and guiding interventions. The UK published weekly estimates of the reproduction number in the UK starting in May 2020 which are formed from multiple independent estimates. In this paper, we describe methods used to estimate the time-varying SARS-CoV-2 reproduction number for the UK. We used multiple data sources and estimated a serial interval distribution from published studies. We describe regional variability and how estimates evolved during the early phases of the outbreak, until the relaxing of social distancing measures began to be introduced in early July. Our analysis is able to guide localized control and provides a longitudinal example of applying these methods over long timescales. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

How can consultant-led childbirth care at time of delivery be maximised? A modelling study

OBJECTIVE: The Royal College of Obstetricians and Gynaecologists has advised that consolidation of birth centres, where reasonable, into birth centres of at least 6000 admissions per year should allow constant consultant presence. Currently, only 17% of mothers attend such birth centres. The objective of this work was to examine the feasibility of consolidation of birth centres, from the perspectives of birth centre size and travel times for mothers. DESIGN: Computer-based optimisation. SETTING: Hospital-based births. POPULATION OR SAMPLE: 1.91 million admissions in 2014-2016. METHODS: A multiple-objective genetic algorithm. MAIN OUTCOME MEASURES: Travel time for mothers and size of birth centres. RESULTS: Currently, with 161 birth centres, 17% of women attend a birth centre with at least 6000 admissions per year. We estimate that 95% of women have a travel time of 30 min or less. An example scenario, with 100 birth centres, could provide 75% of care in birth centres with at least 6000 admissions per year, with 95% of women travelling 35 min or less to their closest birth centre. Planning at local level leads to reduced ability to meet admission and travel time targets. CONCLUSIONS: While it seems unrealistic to have all births in birth centres with at least 6000 admissions per year, it appears realistic to increase the percentage of mothers attending this type of birth centre from 17% to about 75% while maintaining reasonable travel times. Planning at a local level leads to suboptimal solutions.