Modelling patient flows as an aid to decision making for critical care capacities and organisation.

Using real data from a number of hospitals, we predicted the patient flows following a capacity or organisational change. Clinically recognisable patient groups obtained through classification and regression tree analysis were used to tune a simulation model for the flow of patients in critical care units. A tuned model which accurately reflected the base case of the flow of patients was used to predict alterations in service provision in a number of scenarios which included increases in bed numbers, alterations in patients' lengths of stay, fewer delayed discharges, caring for long stay patients outside the formal intensive care unit and amalgamating small units. Where available the predictions' accuracy was checked by comparison with real hospital data collected after an actual capacity change. The model takes variability and uncertainty properly into account and it provides the necessary information for making better decisions about critical care capacity and organisation.

Mathematical modelling and simulation for planning critical care capacity.

Using average number of patients expected in a year, average length of stay and a target occupancy level to calculate the number of critical care beds needed is mathematically incorrect because of nonlinearity and variability in the factors that control length of stay. For a target occupancy in excess of 80%, this simple calculation will typically underestimate the number of beds required. More seriously, it provides no quantitative guidance information about other aspects of critical care demand such as the numbers of emergency patients transferred, deferral rates for elective patients and overall utilisation. The combination of appropriately analysing raw data and detailed mathematical modelling provides a much better method for estimating numbers of beds required. We describe this modelling approach together with evidence of its performance.

Practical models for the care of HIV and AIDS patients.

Mathematical models for infectious diseases are of limited use in providing practical help to health professionals. In this paper we discuss computer models developed jointly by operational research mathematicians and clinicians to meet this need. We use the term 'operational modelling' to describe this pragmatic approach. The models can aid decision-making at a resource planning level and can also be used by clinicians to monitor and improve patient care. The models incorporate uncertainty and variability and are therefore mathematically complex, but are easy to use and provide a great deal of useful information about morbidity and resource use.

Simulation modelling for HIV infection and AIDS.

In this paper we describe a computer model developed jointly by mathematicians and medical consultants. The aim of the model is to provide practical help to people involved with caring for HIV-infected patients. The program is easy to use and can provide a wide variety of output, ranging from resource requirements and costs to detailed clinical information. The model uses the technique of computer simulation to study the progression of HIV-related diseases in a set of patients. The model can help planners concerned with the broad issues of health care provision, as well as clinical users whose main interest is the management and treatment of individual patients. The model is currently being tested in the Department of Genito-Urinary Medicine in the Royal Victoria Hospital, Bournemouth. The potential capability of the model is illustrated by some results from program runs using data from a set of Bournemouth patients. We argue that the power and flexibility of computer simulation as a technique for dealing with uncertainty and variability is especially appropriate in the case of HIV and AIDS.