A mathematical modelling approach for systems where the servers are almost always busy.
Computational and Mathematical Methods in Medicine
Hindawi Publishing Corporation
Copyright © 2012 Christina Pagel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The design and implementation of new configurations of mental health services to meet local needs is a challenging problem. In the UK, services for common mental health disorders such as anxiety and depression are an example of a system running near or at capacity, in that it is extremely rare for the queue size for any given mode of treatment to fall to zero. In this paper we describe a mathematical model that can be applied in such circumstances. The model provides a simple way of estimating the mean and variance of the number of patients that would be treated within a given period of time given a particular configuration of services as defined by the number of appointments allocated to different modes of treatment and the referral patterns to and between different modes of treatment. The model has been used by service planners to explore the impact of different options on throughput, clinical outcomes, queue sizes, and waiting times. We also discuss the potential for using the model in conjunction with optimisation techniques to inform service design and its applicability to other contexts.
This project was funded by the National Institute for Health Research Service Delivery and Organisation programme (Project no. 08/1504/109). The views expressed in this publication/presentation are those of the authors and not necessarily those of the NHS, the NIHR, or the Department of Health. The NIHR SDO programme is funded by the Department of Health.
Research Support, Non-U.S. Gov't
This is the final version of the article. Available from Hindawi Publishing Corporation via the DOI in this record.
Vol. 2012, pp. 290360 -
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