Erlang could have told you so—A case study of health policy without maths

Abstract

Little consideration is given to the operational reality of implementing national policy at local scale. Using a case study from Norway, we examine how simple mathematical models may offer powerful insights to policy makers when planning policies. Our case study refers to a national initiative requiring Norwegian municipalities to establish acute community beds (municipal acute units or MAUs) to avoid hospital admissions. We use Erlang loss queueing models to estimate the total number of MAU beds required nationally to achieve the original policy aim. We demonstrate the effect of unit size and patient demand on anticipated utilisation. The results of our model imply that both the average demand for beds and the current number of MAU beds would have to be increased by 34% to achieve the original policy goal of transferring 240 000 patient days to MAUs. Increasing average demand or bed capacity alone would be insufficient to reach the policy goal. Day-to-day variation and uncertainty in the numbers of patients arriving or leaving the system can profoundly affect health service delivery at the local level. Health policy makers need to account for these effects when estimating capacity implications of policy. We demonstrate how a simple, easily reproducible, mathematical model could assist policy makers in understanding the impact of national policy implemented at the local level.