The Dynamics of Treatment and Capacity

Abstract

All the case studies in this book are based on system dynamic models representing patient pathways as stock-flow (or ‘bathtub’) systems. This chapter will introduce these fundamental building blocks and their use in a simple, but insightful, model of a hospital relating 7 key performance variables. This model lies at the heart of many of the project models described in the book.

Appendix: The Answer to the Exercise in Fig. 2.2

Answers:

• 1. Day 9 The number of admissions per day is shown by the dotted line (2), which peaks at week 9

• 2. Day 16 The number of discharges per day is shown by the dashed line (1), which peaks at week 16

• 3. Day 14 During the first 14 days the number of admissions is greater than the number of discharges and after that time the number of discharges is greater than the number of admissions. So, most people are in the hospital at day 14.

• 4. Day 19 This is perhaps the trickiest of the questions. We know from answer 3 that the number of people in the hospital goes up until day14 and down until day 19. But we do not know by how much. To find out, it is necessary to estimate whether more people are admitted before day 14 than are discharged after day 14. That is whether the area between the two curves up to day 14 is greater or less than the area between the two after that time. Observation will show that it is greater. More people leave after day 14 than are admitted before day 14. So, the fewest people are in the hospital after 19 day.

Answers 3 and 4 are made much clearer by studying the graph of inpatients at the top of the answer, which is the result of the net flow of admissions and discharges.