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Mathematical model can reduce waiting times in healthcare

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15 January 2025
Elderly people often stay unnecessarily long on an expensive hospital bed when admitted to a hospital. This is because there is not enough space in follow-up care. This is disadventageous for the patient and also burdensome for the healthcare system. Mathematician Rebekka Arntzen developed a model to improve the flow to follow-up care.

Flow problems are partly caused by long waiting times for nursing homes, which put pressure on the care system 'upstream'. Currently, nursing home waiting lists are managed by the institutions themselves, without central coordination.

Shorter waiting times
With central coordination, you have to choose which patient to prioritise, based on factors such as waiting time and the patient's preference for a particular nursing home. Arntzen developed a mathematical method that calculates which person is best matched with an available bed.

Using a computer simulation, she mimicked eldercare processes and simulated alternatives. She also used microdata from Statistics Netherlands (CBS), and conducted interviews and surveys. The results of the simulation study show that it is possible to make optimal use of capacity, reduce waiting times and meet the wishes of the elderly at the same time.

Queue in supermarket
According to Arntzen, it would therefore be better for long-term care to manage queues centrally. 'The current situation can be compared to a supermarket where you are stuck in a slow queue,' she explains. 'Meanwhile other queues go faster, without allowing you to switch. This also happens at nursing homes, only less visible. By centralising waiting lists, we get more control over waiting times and flexibility in placement, such as with an allocation model.'

When it comes to short-term care, Arntzen says there is not always a shortage of beds, but often of admission options. 'Investing in good admission options prevents many unwanted, expensive hospital admissions, in which elderly people often deteriorate unnecessarily. These improvements make care more efficient and more humane.'

Arntzen defends her PhD thesis on 12 February.

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