Availability of a pediatric trauma center in a disaster surge decreases triage time of the pediatric surge population: a population kinetics model

Abstract

Background: The concept of disaster surge has arisen in recent years to describe the phenomenon of severely increased demands on healthcare systems resulting from catastrophic mass casualty events (MCEs) such as natural disasters and terrorist attacks. The major challenge in dealing with a disaster surge is the efficient triage and utilization of the healthcare resources appropriate to the magnitude and character of the affected population in terms of its demographics and the types of injuries that have been sustained.

Results: In this paper a deterministic population kinetics model is used to predict the effect of the availability of a pediatric trauma center (PTC) upon the response to an arbitrary disaster surge as a function of the rates of pediatric patients' admission to adult and pediatric centers and the corresponding discharge rates of these centers. We find that adding a hypothetical pediatric trauma center to the response documented in an historical example (the Israeli Defense Forces field hospital that responded to the Haiti earthquake of 2010) would have allowed for a significant increase in the overall rate of admission of the pediatric surge cohort. This would have reduced the time to treatment in this example by approximately half. The time needed to completely treat all children affected by the disaster would have decreased by slightly more than a third, with the caveat that the PTC would have to have been approximately as fast as the adult center in discharging its patients. Lastly, if disaster death rates from other events reported in the literature are included in the model, availability of a PTC would result in a relative mortality risk reduction of 37%.

Conclusions: Our model provides a mathematical justification for aggressive inclusion of PTCs in planning for disasters by public health agencies.

Figure 1

Qualitative behavior of surge (blue), admitted (red), and discharged (green) populations with time as predicted by Equations 10, 12 and 13. Curves are normalized for clarity.

Figure 2

Behavior of surge (blue), admitted (red), and discharged (green) populations with time in the maximum capacity model described by Equations 16-18. Curves are not normalized or scaled.

Figure 3

Behavior of pediatric cohort of the surge (top panel), admissions to adult center (second panel), admissions to pediatric center (third panel), and discharged patients (fourth panel) with time as predicted by the maximum capacity with PTC model, Eqs. 40-50. Uppercase letters indicate boundary conditions for the appropriate differential equations; see text for details.

Figure 4

Effect of changing the constraint on τ = t2-t1 on the fitted values of the rates for the maximum capacity model. Error bars represent one standard deviation; see text for details.

Figure 5

Time needed to admit (t2, panels A and B) and definitively treat to discharge (t99, panels C and D) the pediatric surge population for two subsets of the input parameter space. When the pediatric center's admission and discharge rate parameters are uniformly scaled up from zero to the values for the adult center, t2 decreases monotonically but t99 is initially prolonged (A, C). If the PTC discharge rate is set equal to that of the adult center for the pediatric surge patients while the admission and steady-state discharge rates are scaled up from zero to the values for the adult center, t2 (panel B) behaves similarly as in A, but t99 decreases uniformly (D). See text for details.

Figure 6

Qualitative behavior of maximum capacity with PTC model with explicit death rates derived in Appendix B. Blue curve: pediatric surge. Red curve: pediatric patients admitted to adult center. Orange curve: pediatric patients admitted to PTC. Green curve: living discharged patients. Black curve: deceased patients.