Mathematical modelling in health care

We will describe several cases studies that illustrate how we have used modelling to improve the delivery of health care. The studies cover various settings in health care, utilise a variety of mathematical modelling techniques, and include descriptions of the impact of the model on the health care system. The studies can be described briefly as follows. In the financial year 2006/2007, emergency departments (EDs) in Australian hospitals dealt with 5,287,451 presentations. Statistical models have been used to forecast the number of patients served by an ED each month, and to evaluate the impact of changes and innovations introduced to the ED. The operation of an acute care hospital medical service has been described well by a double compartment model. Modification to the basic model facilitates the incorporation of occupancy fluctuations, such as winter peaks, across the year. These models can improve strategic decision making in relation to hospital beds. At a more aggregated level, a cohort Markov model was used to identify the most cost-effective screening programme for cervical cancer. The model describes the development of precancerous lesions and progression via multiple stages to the advanced form of cervical cancer, and subsequent death. Cancer may be diagnosed at any time, via screening or clinical presentation with symptoms, at which point treatment may be initiated that will alter the natural history of the disease. The model was used to evaluate a large number of screening options, for which it would be infeasible to conduct clinical studies. Transition care is a form of health care for hospital patients who have finished their stay in an acute care setting but are not be able to return home. Queueing theory has been used to estimate the number of places required for a new transition care facility in a hospital. This example demonstrates how modelling has been used in applying for funds to support new developments in a hospital. These examples illustrate the potential for applying mathematical modelling and simulation in health care.