Mathematical modelling and simulation for planning critical care capacity

Area of Science:

• Healthcare Management
• Operations Research
• Critical Care Medicine

Background:

• Traditional methods for calculating critical care bed needs rely on simplified averages.
• These methods often fail to account for the inherent variability and nonlinearity in patient flow and length of stay.
• This can lead to significant underestimation of required beds, particularly at higher occupancy targets (e.g., >80%).

Purpose of the Study:

• To identify the mathematical inaccuracies in simple bed calculation methods.
• To demonstrate the limitations of these methods in predicting critical care demand.
• To present and validate a more robust approach using data analysis and mathematical modeling for bed requirement estimation.

Main Methods:

• Analysis of raw patient data to understand variability in length of stay and demand.
• Development of detailed mathematical models simulating critical care patient flow.
• Comparison of model outputs with traditional calculation methods.

Main Results:

• Simple calculations significantly underestimate bed needs at occupancy levels above 80%.
• Traditional methods fail to provide insights into emergency transfers, elective deferrals, and overall utilization.
• The proposed modeling approach accurately estimates bed requirements and provides quantitative demand insights.

Conclusions:

• The conventional method of calculating critical care beds using averages is mathematically flawed.
• Accurate estimation of critical care beds requires sophisticated data analysis and mathematical modeling.
• This advanced approach offers better quantitative guidance for managing critical care resources and demand.