OUTPUT ANALYSIS

Running the simulation model with the arrival rates previously calculated resulted in an average wait time of around 54 days for regular impatient beds and an average of about 48 days for ICU beds. Since this data is from the peak of the COVID-19 outbreak, it makes sense that the wait times would be so long as all hospitals were over capacity during this time period. In order to decrease the waiting time for both regular and ICU beds, the number of resources available (number of beds) will have to increase. To determine the optimal number of resources to decrease the wait times of both the ICU and regular beds to 1 hour or less, the group tested many resource levels over various simulation runs as shown in the sensitivity analysis.

This simulation focuses on the usage condition and treatment time of the regular bed and ICU bed since the mean waiting time of beds shows the affordability of the healthcare system. Furthermore, simulation on the affordability of the health care system could indicate the reasons that may cause resource shortages in the future. From the statistics on the resource shortage found in the simulation result, improvement suggestions could be concluded. This simulation doesn’t consider the number of deaths or the life of the patient after the treatment since there are various factors that may cause patient death or life after treatment from both regular bed and ICU bed.

6.1 Input Uncertainty Quantification

In order to quantify the input model estimation uncertainty, the bootstrap method was used on various samples of input models. For each sample, the simulation was run and the batch-to-batch variation of the output was estimated. Bootstrapping randomly samples the data with replacement to create a new bootstrap dataset. Then, the maximum likelihood calculation previously done in the parameter estimation was repeated on the new bootstrapped dataset. Additional iterations are completed for many bootstrapped datasets. This bootstrapped data was used later in Section 6 (Output Analysis) for sensitivity analysis.

6.2 Sensitivity Analysis

Sensitivity Analyses determine the sensitivity of the simulation outputs to each input model estimation uncertainty. It is beneficial for complex systems which have many sources of uncertainty in order to determine which sources of uncertainty deserve the most attention. It also provides guidance on which aspects of the model require more information to improve accuracy.

For each replication, the confidence intervals of the ICU and regular bed wait times for patients was calculated. This is shown in the data below. These confidence intervals were calculated using the initial dataset (not bootstrapped).

As can be observed, the non-bootstrapped data has a very large CI range meaning that there is a lot of uncertainty surrounding the estimation. In order to improve the accuracy of the simulation, the dataset was bootstrapped and then the CIs were recalculated with this new data.

After, to determine the impact of the bootstrapping on model performance, the confidence intervals of the bootstrapped data were calculated. In the table below, the left side represents the wait times for both types of beds before the patient is able to be serviced. On the right side, the CIs are provided for the service time of patients after they are assigned a bed. Compared to the CIs calculated with the non-bootstrapped data in Tables 6 and 7, after the bootstrap, the CIs decreased significantly as seen in Table 8. This means that there is less uncertainty in the model and the group can be more confident in the results of the model. The first two rows of the table show the standard CIs without any adjustments made to the system. The next two rows represent the CI when the arrival rate is fixed. When arrival rates of patients are fixed, the CI of the ICU wait time decreases while the CI for the regular and ICU service time along with the regular wait time remains constant. On the other hand, the last two rows represent the instance when the service time (bed time) is fixed. In this case, the CI for regular and ICU bed wait times remains similar while the CI for regular and ICU service time decreases compared to the first two rows of data. This logically is expected and validates that our simulation is working correctly.