Disaster preparedness and response in the operating room is based on what approach

@inproceedings{Nouaouri2011OperatingRS,
  title={Operating room scheduling under unexpected events : the case of a disaster},
  author={Issam Nouaouri and J-C. Nicolas and Daniel Jolly},
  year={2011}
}

Disaster like terrorist attack, earthquake, and hurricane, often cause a high degree of damage. Hundreds of people may be affected. Hospitals must be able to receive, in a short period, injured persons for medical and surgical treatment, using available resources and facilities. In such situations different disruptions widely perturb the execution of the established plans. Then medical resources optimization is fundamental to save human lives. Our works focus on operating rooms scheduling… 

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Managing urgent care in hospitals

  • N. Borgman
  • Medicine, Political Science

  • 2017

This thesis addresses a number of challenges related to the provision of care for non-elective patients in hospitals in the Netherlands, and addresses planning problems encountered at various hospital departments where non- elective patients are treated.

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References

SHOWING 1-10 OF 23 REFERENCES

Lessons in logistics from Somalia.

  • D. Kemball-CookR. Stephenson
  • Business

    Disasters

  • 1984

There is a prime need for logistics to be centralized in a single organization at the start of major emergencies, and it is suggested that a new or existing part of the United Nations family be given a 'brief for in-country logistics' to become a UN Emergency Logistics Office.

Introduction

Hospital systems are at the core of disaster resilience because they must provide timely critical healthcare services to communities during an emergency response. Because cities are becoming larger and more densely populated, natural disasters are impacting public health on a larger scale. A database including the most 21,000 devastating disasters worldwide since 1900 indicates that 50% of disasters with the largest number of injuries occurred only during the last 20 years1. Natural disasters such as earthquakes, landslides, floods, typhoons put heavy demands on hospital systems because these disasters can cause thousands or even tens of thousands of injuries in a short timespan. At the same time, natural disasters cause massive disruptions to hospital systems by damaging their supporting infrastructure. For example, the M 7.6 1999 Turkey earthquake caused ~50,000 injuries in Izmit and disrupted 10 major hospitals, which required the relocation of most patients from these hospitals2.

Natural disasters also demand large mobilizations of patients. For example, 2k to 3k patients had to be transferred between hospitals after the M 8.8 2010 Chile earthquake3. In large urban centers, such massive mobilization of patients requires an organized and system-level response to treat them timely. Yet, evidence shows that responses are often not the result of a global, system-level strategy but rather local and haphazard4. After the M 6.7 1994 Northridge earthquake, two hospitals transferred their patients to a non-functional hospital, thus the patients had to be transferred a second time5.

Recognizing the importance of organized and system-level hospital response, the World Health Organization [WHO] and Pan-American Health Organization [PAHO] urge countries to institute policies to strengthen capacities and enhance coordination in the hospital system to make efficient use of resources at national and regional levels during emergency response6,7. To effectively develop measures for capacity-enhancing prioritization and resource sharing and allocation, national and regional governments require information based on robust methodologies that can characterize hospitals’ emergency response as an interconnected system rather than as isolated units. However, research has not yet focused on developing such system-level methodologies that can support governments to elaborate effective plans for emergency response and quantify their potential benefits in treating patients more effectively and saving lives.

Instead, recent studies have primarily focused on modeling emergency response only on a single-hospital scale. Some studies rely on disaster analytics to evaluate post-disaster functionality of the supporting infrastructure in the individual hospitals8,9,10,11. Other studies use emergency medicine modeling tools, such as discrete event simulation and flow models, to characterize emergency response and evaluate post-disaster resource allocation but also on a single-hospital scale12,13,14,15. Lack of methods and high-resolution disaster risk data have hindered the extension of single-hospital scale analyses to system-level analyses on an urban scale. As a result, regional emergency response plans have not effectively addressed capacity-enhancing prioritization and resource sharing and allocation in hospital systems, especially in large and complex urban centers.

To demonstrate the benefits of organized, system-level responses, we present findings from applying a methodology that characterizes the disaster emergency response of hospitals as a system. Our integrative methodology combines models of multiseverity earthquake casualty estimation16,17 and post-earthquake hospital functionality with a proposed network flow model. The network flow model captures the system behavior of emergency responses through the evaluation of patient treatment, triage processes, and patient transfers across a large number of hospitals, which establishes a fundamental difference from existing formulations focused on analyses on a single-hospital scale.

We apply the methodology to the city of Lima, Peru, subjected to a M 8.0 earthquake scenario. We selected Lima because it has a high seismic risk and it has recently built a unique data set containing high-resolution hospital vulnerability. We use city-wide data on the seismic vulnerability of >1.5 M buildings in Lima to estimate casualties and data including the seismic vulnerability of 41 public hospital campuses [composed of +700 buildings] and their respective operating rooms and ambulance resources11,18,19.

We propose a metric based on patient waiting times and effective use of ambulances as a performance measure for developing emergency response plans. Our focus is on high-severity injuries that require surgical procedures in operating rooms. We evaluate the spatial distribution of high-severity injuries in the city at a high spatial resolution of 1 km. Then, we compare the spatial distribution of casualties with the distribution of functional operating rooms in the hospital system, identifying the zones more likely to be underserved during the emergency response.

Combining the network flow model with an optimization formulation, we assess the performance of four alternative emergency response plans to treat the patients in the city. The first and second emergency plans are baseline strategies with limited levels of coordination that enable hospitals to respond mostly locally. The third and fourth emergency plans are strategies with higher levels of coordination at the system level and that use our proposed formulation to optimize the effectiveness of the response. In both strategies, hospitals respond as a system by sharing their ambulances among themselves to transfer patients according to post-earthquake needs. With the fourth strategy, emergency medical teams [EMTs] supply the system with additional mobile operating rooms in key locations in the city. Through the Action Plan for Humanitarian Assistance, the WHO and PAHO require countries to elaborate policies for deploying EMTs to assist people affected by emergencies and disasters20, thus, this study aims to directly inform policies for EMT deployment in countries with high seismic risk.

Our results show the improved performance of the third and fourth strategies owing to their high-coordination capacities leading to shorter patient waiting times and more effective ambulance usage and patient transfers. We also identify the most important roads for patient transfers, the ones that connect zones with lower hospital capacity to zones with higher capacity in the city. This research represents a first-cut assessment of the effectiveness of emergency response policies to inform city-scale decision-making aiming to more effective treatment of patients during an emergency response to a major earthquake.

Results

Earthquake scenario

Lima is a large city with a population close to 10 million people, where previous large earthquakes21 have caused large numbers of casualties22. In our case study, we assess an earthquake scenario simulated according to the seismotectonics of the 1940 M 8.0 earthquake, which occurred in close proximity to Lima23. Figure 1 shows the estimated rupture area of the 1940 earthquake and its proximity to the city. Our methodology estimates the impact of this disaster scenario on the demands on healthcare by quantifying earthquake casualties and on the capacity of healthcare by quantifying the post-earthquake reduction in functionality in the hospital system.

Fig. 1: Earthquake scenario representing the M 8.0 1940 earthquake in Lima.

The earthquake occurred in the subduction fault in the coast of Lima and caused widespread damage to the city22,70. The estimated area of fault rupture is shown in red. The edge dimensions were estimated with empirical formulas63. The fault plane dips 15, where the edge underneath the coast is deeper than the edge under the ocean. The median peak ground acceleration [PGA] is also estimated with empirical formulas64. The shaking attenuates for regions further away from the rupture in the fault plane. Lima city and its districts are delimited by the black shapes. Source data are provided as a Source Data file, and the base map layer is available under a //www.openstreetmap.org/copyright Open Database Licence [© OpenStreetMap Contributors].

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Earthquake casualties

We estimate that on average close to 4.7k people will require surgical procedures in operating rooms after the M 8.0 earthquake. This estimate results from applying a probabilistic model that utilizes high-resolution building seismic vulnerability data, population distribution, and soil conditions to evaluate multiseverity earthquake casualties caused by widespread building damage16,17 [see “Methods”]. Earthquake injuries can have different severity degrees, ranging from small bruises to more serious spinal cord injuries24,25. The 4.7k patients requiring surgical procedures will have high-severity injuries such as compound bone fractures, punctured organs, or crush syndrome with open wounds, thus needing timely interventions for stabilization and treatment.

Our results are designed for an earthquake occurring at nighttime. This scenario represents a potential worst-case scenario because it is when most people are inside residential buildings, which are particularly vulnerable in Lima. Predominantly, the city’s periphery has vulnerable residential infrastructure as a result of poor construction practices and lack of seismic code enforcement26,27. Fig. 2 shows the spatial distribution of the average number of patients who will require surgical procedures for the nighttime scenario. A comparison with the spatial distribution of nighttime population density in Lima [Supplementary Figure 1] indicates that many of these patients are located in high-density zones. Because earthquakes have a uniform distribution of occurrence during a day, this scenario has a slightly higher likelihood of occurring than the other two important earthquake scenarios to consider: commuting hours from 6 am to 8 am and from 4 pm to 8 pm, and working hours from 8 am to 4 pm16,17. The Methods section includes a description of the data requirements to fully evaluate scenarios at other times with our formulation, and the Supplementary Information includes a discussion of their potential results [see Supplementary Figures 2 and 3].

Fig. 2: Casualty scenario for M 8.0 earthquake occurring at nighttime in Lima.

The plot shows the spatial distribution in km2 of the mean number of earthquake injuries requiring surgical procedures after the M 8.0 seismic event. The intervals represent quantiles [20th-percentile increments] on the spatial data. Source data are provided as a Source Data file, and the base map layer is available under a //www.openstreetmap.org/copyright Open Database Licence [© OpenStreetMap Contributors].

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Post-earthquake hospital capacity

We estimate that on average only 87 of 182 total hospital operating rooms [48%] will be functional after the M 8.0 earthquake. We verified that our results were consistent with the reductions of hospital capacities in past earthquakes. For example, similar to our predicted high levels of capacity reduction, the M 8.0 2007 Pisco earthquake in Peru reduced the hospital bed capacity to 38%28. Our estimates of capacity reduction result from performing a probabilistic earthquake simulation on a high-resolution data set [see Methods]. The data set includes the structural vulnerabilities of +700 buildings belonging to 41 healthcare campuses18, the operating room resources, and Hospital Safety Index [HSI] of each campus. HSI is a metric created by WHO to measure post-disaster functionality potential due to multiple factors such as backup water, power, medical resources, and hospital accessibility29. This unique data set in combination with the earthquake simulation enables us to capture the residual hospital functionality on a large urban scale.

  Fig. 3a shows the spatial distribution of both the operating rooms in the data set and the average predictions of operating rooms after the earthquake. Both spatial distributions are heavily uneven across the city. In the data set, 95 operating rooms [52%] are concentrated in only four centric districts, Lima, Breña, La Victoria, and Jesús María, whose summed areas represent = 0, i Γ. In the discharge nodes, bi[t] represent the number of patients who finish their treatment and exit the hospital at time t, thus they are analyzed as sink nodes with non-positive flows: bi[t] < = 0, i Λ. We assume that patients who finish the treatment process and exit the hospital do not to return to the hospital system during the time horizon tf. Each graph edge is associated to a flow of patients xi,j[t] that leaves node i at time t to go to node j. In this formulation, edges fully connect the triage nodes to allow hospitals to redistribute their patient loads to potentially any other hospital within the system according to their available ambulances. In addition, each triage node is connected to its respective discharge node to represent the patient treatment process within a hospital. Fig. 7 shows the edges and respective flows between triage nodes from different hospitals and between triage and discharge nodes within same hospitals for the system with three hospitals. At each time t, the flow xi,j[t] has a maximum bound ui,j[t] and a travel time τi,j[t]. In this discrete formulation, it is considered that the flow xi,j[t] leaves the node i at time t and reaches the node j at time t + τi,j[t].

For the edges connecting triage areas, ui,j[t] represents the maximum number of patients who can be transported from triage i to triage j in a different hospital according to the available transportation resources [e.g., ambulances available in the hospital], and τi,j[t] is the transportation time of the patients from triage i to triage j. For the application to Lima, ui,j[t] and τi,j[t] in these edges were defined according to the ambulance capacities in each hospital and the travel times from pre-earthquake traffic conditions, respectively. When vulnerability data for the transportation system in Lima is available, our model will be able to leverage existing risk models for transportation systems50 to adjust travel times to post-earthquake traffic conditions.

For the edges connecting triage nodes i with their respective discharge nodes j = i + nh, \[{u}_{i,i+{n}_{h}}[t]\] represents the maximum number of patients who can be treated according to the available medical resources for the type and severity of the patients’ injuries, and \[{\tau }_{i,i+{n}_{h}}[t]\] is the treatment time. For the application to Lima, ui,j[t] and τi,j[t] in these edges were defined according to the functional operating rooms in each hospital and average treatment times in operating rooms in previous earthquakes51.

In addition, we define yi[t] as a storage variable at each triage node to represent the patients who wait in the hospital queue to either be treated within the hospital or be transported to another hospital with more available resources.

Optimization of performance metric

We evaluate both waiting times and effective use of ambulances as the system performance metric, thus the metric includes two objective functions. The first objective function C1[X] measures waiting time across the city as the average time that a patient would take since the earthquake until completing treatment in the operating room.

$${C}_{1}[{\bf{X}}]=\frac{{\sum }_{t\in {\bf{T}}}{\sum }_{\begin{array}{c}i\in {\boldsymbol{\Gamma }},\\ j = i+{n}_{{\rm{h}}}\end{array}}\{t+{\tau }_{i,j}\}\times {x}_{i,j}[t]\times dt}{{\sum }_{t\in {\bf{T}}}{\sum }_{i\in {\boldsymbol{\Gamma }}}{b}_{i}[t]}$$

[1]

X represents a vector containing all the decision variables of flow xi,j[t] in edges and the storage yi[t] in the triage nodes. The numerator of C1[X] represents the total number of patients passing through the operating rooms [from each triage node, i Γ to the corresponding discharge node j = i + nh Λ] multiplied by their respective times to complete treatment, whereas the denominator is the total number of patients arriving to the triage areas. The time horizon tf is carefully chosen to have enough modeling time to treat the patients. However, in few simulations with significant number of patients and not many functional operating rooms, a couple of terms are added to the numerator, one with the remainder patients in the triage areas, tf × ∑iΓyi[tf] × dt, and another with the remainder patients in the ambulances, \[{t}_{{\rm{f}}}\times {\sum }_{i\in {\boldsymbol{\Gamma }}}{x}_{i,i+{n}_{{\rm{h}}}}[{t}_{{\rm{f}}}]\times dt\], in order to properly incorporate the unmet demands at the end of the simulation into C1[X].

The second objective function measures ambulance usage as the total number of patients transported in ambulances. The objective function C2[X] is normalized by the total number of patients analogously to C1[X].

$${C}_{2}[{\bf{X}}]=\frac{{\sum }_{t\in {\bf{T}}}{\sum }_{i\in {\boldsymbol{\Gamma }}}{\sum }_{j\in {\boldsymbol{\Gamma }}}{x}_{i,j}[t]\times dt}{{\sum }_{t\in {\bf{T}}}{\sum }_{i\in {\boldsymbol{\Gamma }}}{b}_{i}[t]}$$

[2]

We define a system cost C[X] as a weighted sum of C1[X] and C2[X] to find a Pareto-optimal solution.

$$C[{\bf{X}}]={\alpha }_{1}\times {C}_{1}[{\bf{X}}]+{\alpha }_{2}\times {C}_{2}[{\bf{X}}]$$

[3]

After assessing multiple α1 and α2 values, we minimized C[X] using values of 0.90 and 0.1, respectively. Smaller α2 values resulted in inefficient ambulance usage with small reductions in waiting times, requiring some patients to be transferred multiple times in ambulances before being treated. Larger α2 significantly increased waiting times, thus these α2 values do not appropriately represent that the priority in the formulation is to minimize waiting times over to use ambulances with efficiency. We find the best set of decisions \[\hat{{\bf{X}}}\], vector that contains the values of flow variables xi,j[t] and storage variables yi[t] which minimize C[X].

$$\hat{{\bf{X}}}={{\rm{argmin}}}_{{x}_{i,j}[t];{y}_{i}[t]}\quad C[{\bf{X}}]$$

[4]

The decision variables are subject to the constraints in Equations [5], [6], [7], and [8]. Equation [5] represents patient flow conservation, which guarantees that all the patients coming into the hospital system stay within the system until they leave through the discharge nodes.

$${x}_{i,i+{n}_{{\rm{h}}}}+{\sum }_{j\in {\boldsymbol{\Gamma }}}{x}_{i,j}[t]-{\sum }_{j\in {\boldsymbol{\Gamma }}}{x}_{j,i}[t-{\tau }_{i,j}[t]]+{y}_{i}[t+dt]-{y}_{i}[t]=b[i],\quad \forall i\in {\boldsymbol{\Gamma }},t\in {\bf{T}}$$

[5]

Equations [6] and [7] represent flow capacity constraints. Equation [6] ensures that the people in the operating rooms do not exceed the unitary capacities \[{u}_{i,i+{n}_{{\rm{h}}}}\], where \[{u}_{i,i+{n}_{{\rm{h}}}}\] is estimated as the number of functional operating rooms in the hospital i over the number of surgeries per day. We assumed that each surgery takes 4 hours, and that hospitals will be functional 24 hours during the emergency response using multiple personnel shifts. Such treatment rate equals the rates in foreign field hospitals after the 2004 Indonesia earthquake/tsunami51.

$$0\le \frac{{x}_{i,i+{n}_{{\rm{h}}}}[t]}{{u}_{i,i+{n}_{{\rm{h}}}}}\le 1,\quad \forall i\in {\boldsymbol{\Gamma }},t\in {\bf{T}}$$

[6]

Equation [7] ensures that the patient transfers do not exceed the total unitary transportation capacities in a hospital, where ui,j is the unitary capacity if all ambulances of a hospital were only transferring patients from triage i to j. ui,j equals the number of ambulances in the hospital times the number of patients transported per ambulance trip over the number of round trips that an ambulance can make from triage node i to j. We retrieved travel time information from Google Maps API to estimate the round trip numbers and assumed that each ambulance trip can take up to two patients.

$$0\le {\sum }_{j\in \Gamma }\frac{{x}_{i,j}[t]}{{u}_{i,j}}\le 1,\quad \forall i\in {\boldsymbol{\Gamma }},t\in {\bf{T}}$$

[7]

Equation [8] ensures that the number of patients waiting in the hospitals’ triage queues are properly represented by a non-negative number.

$$0\le {y}_{i}[t],\quad \forall i\in {\boldsymbol{\Gamma }},t\in {\bf{T}}$$

[8]

Equations [6], [7], and [8] introduce a model relaxation. Whereas the number of patients who are treated, transported or waiting in the queue can only be non-negative integers, the formulation expands the variables’ domain to include real numbers. This relaxation ensures that the formulation is tractable. Thus, because the cost and the constraint functions are linear combinations of the decision variables, we solve this minimization as a linear programming problem using the simplex algorithm in GLPK of the cvxopt implementation in Python52.

Model adaptation for baseline strategies 1 and 2

Both baseline strategies have limited coordination capacity and only allow each hospital to transfer patients to only one single hospital with functional operating rooms instead of multiple ones. Thus, to represent these strategies, the model ignores multiple transfer edges in the flow model, reducing the elements of the edge set E. In the first baseline strategy, only the edges going from hospitals without functional operating rooms to the closest hospitals are activated. In the second baseline strategy, only the edges going from hospitals without functional operating rooms to the hospital with the largest number of functional operating rooms are activated.

Because the model is solved multiple times according to the number of patients and functional operating rooms in the earthquake simulation, then the edge connectivity varies from simulation to simulation. With strategies 1 and 2, the number of edges in the model is significantly reduced, thus we modeled larger time horizons. We selected a time horizon tf of 100 days, which is sufficiently long period to treat all earthquake patients in most simulations, and a time step dt of 1 day.

Model adaptation for sharing ambulances

Strategy 3 does not need to disconnect edges in the model. Yet, it modifies the transportation edges’ capacity constraints to enable hospitals to share ambulance resources. Thus, the constraint in Equation [7] is relaxed as follows.

$$0\le \sum _{i\in {\boldsymbol{\Gamma }}}{a}_{i}\sum_{j\in {\boldsymbol{\Gamma }}}\frac{{x}_{i,j}[t]}{{p}_{i,j}}\le \sum_{i\in {\boldsymbol{\Gamma }}}{a}_{i},\quad \forall t\in {\bf{T}}$$

[9]

Equation [9] ensures that unitary transportation capacities are not exceeded at a system level at each time step, where ai represents the number of ambulances of hospital i. All the other constraints remain the same. Because modeling this policy requires higher edge connectivity than the baseline strategies and thus has more computational demands, the time horizon tf was reduced to 40 days. It was verified that such a variation did not affect the optimization because less modeling time was needed as a result of shorter optimal waiting times with the strategies 3 and 4 [Fig. 5]. The time step dt was kept equal to 1 day.

Model adaptation for deployment of more operating rooms

Strategy 4 requires an additional modification to the constraint on the operating room capacity in Equation [6]. This strategy allows EMTS to increase hospital capacities by introducing additional mobile operating rooms in close proximity to them as follows.

$$0\le \frac{{x}_{i,j}[t]-{q}_{i}}{{u}_{i}}\le 1,\quad \forall i\in {\boldsymbol{\Gamma }},j=i+{n}_{h}\in {\boldsymbol{\Lambda }},t\in {\bf{T}}-\{0,dt,\ldots ,{t}_{{\rm{s}}}\}$$

[10]

Equation [10] ensures that hospitals can increase their unitary operation room capacities by qi after the time ts at which the operating rooms in the field hospitals are deployed in the city. In addition, the sum of the additional resources distributed across the system cannot exceed the total capacity Q supplied by all the field hospitals in the region as follows.

$$0\le \sum_{i\in {\boldsymbol{\Gamma }}}{q}_{i}\le Q$$

[11]

All the other constraints remain the same. These modifications barely change the optimization complexity. Thus, we kept the time horizon equal to 40 days and the time step equal to 1 day.

Earthquake casualty modeling

We utilize an earthquake multiseverity casualty model previously developed by the authors17 to evaluate the spatial distribution of injuries requiring surgical treatment after the M 8.0 earthquake. The model is probabilistic and uses ground shaking estimates to propagate the earthquake intensity to building damage according to the building seismic vulnerability53 and the site-specific soil conditions in Lima54. Next, the model uses information on building occupancy to provide probabilistic estimates of the spatial distribution of injuries and fatalities in the city. The validity of the model results was verified16 by comparing the casualties and fatality levels in the city to empirical formulas55 and with fatality-to-collapse building data from the 2005 Pakistan earthquake56.

The model categorizes injuries into three severities. The second- and third-degree severity require specialized medical attention and hospitalization, however, unlike the second degree, the third one requires immediate rescue and treatment to avoid death57. We considered that 100% of the patients with third-degree injuries, for example, having punctured organs or crush syndrome with exposed wounds, plus 10% of patients with second-degree injuries, for example, having compound bone fractures, will require surgical treatment in operating rooms. We considered that patients arrive to the closest hospital during a period of 4 days after the earthquake in accordance to the evidence from previous earthquakes32. Thus, in the flow model the demand-supply variable bi[t] is larger than 0 in the triage nodes during the first four days after the earthquake. We considered that patients wait in triage zones to until an operating room is available in the hospital or until they are transferred to other hospitals.

Seismic analysis for hospital functionality

We utilize earthquake simulation to model the functionality of operating rooms during the emergency response58. Hospitals are complex infrastructure, whose post-earthquake functionality depends on multiple components: structural damage; damage in mechanical, electrical components and medical equipment; utility failure; shortage of medical supplies [i.e., oxygen, blood], and shortage of medical personnel9,10,14,59. Hospitals with slight structural damage can lose partial or total functionality as a result of damage and loss of the other components of hospitals60.

To capture these effects, we analyzed that the structural vulnerability53 of the +700 buildings belonging to the 41 healthcare campuses in the city according to the earthquake shaking intensity and the soil conditions on site. Then, we used a Bernoulli distribution to model loss of functionality that can occur owing to failure of components different to the hospitals’ structure according the Hospital Safety Index [HSI]. HSI is based on a qualitative evaluation of multiple hospital components including buildings’ nonstructural elements such as equipment and backup medical resources, and technical and organization capacities in the hospitals’ personnel29. HSI has three categories: A, B, and C, ranging from the best to the lowest performance. We used a different Bernoulli distribution for each HSI category. We considered that operating rooms in buildings with no structural damage have 1, 0.75, and 0.5 of functionality probability for categories A, B, and C, respectively, whereas that in buildings with slight structural damage, operating rooms have 0.6, 0.45, and 0.3 of functionality probability. Operating rooms in buildings with larger damage levels were considered completely non-functional.

The 41 campuses in the data set are part of the public healthcare system led by the Peruvian Health Ministry [MINSA] and the Social Security [Essalud]. Even though there is a growing private healthcare system, most of the healthcare services are provided by the public system in Lima61. Physicians who work full time in the public healthcare system often work part-time in the private system62, thus in an emergency, they would aim to provide services in the public system rather than in the private one. We consider that studying the response of the public sector represents a robust starting point to characterize the earthquake emergency response of the hospital system in Lima.

We supplemented the hospitals’ building information with the number of ambulance in each hospitals. Because, a few hospitals have no ambulances, we considered that during the emergency response the local government or private institutions will supply one ambulance to each of these hospitals so that each hospital is able to mobilize patients.

Earthquake shaking

We studied the tectonics of the M 8.0 1940 earthquake and located the rupture area in the region delimited by the earthquake aftershock zone23. We defined the rupture dimensions along the fault strike and dip directions using an empirical function based on subduction zone earthquake data63.

Next, we evaluated the ground shaking in a grid of 1 km × 1 km using site-specific lognormal distributions. We evaluated three ground shaking intensity measures, peak ground acceleration spectral acceleration at 0.3s, Sa[0.3s], and spectral acceleration at 1s, Sa[1.0s]. We selected these intensity measures to better capture the response of multiple typologies of buildings in the inventory according to their predominant period of vibration. The log-mean and log-standard-deviation values of the intensity measures were extracted from empirical formulas that relate magnitude, site distance, and soil conditions to the ground shaking64. We included within-65 and between-66event correlations in the intensity measures. The between-event correlations introduce spatial correlations to the ground shaking.

Model limitations and future work

Our formulation and case study advance the field of earthquake emergency response. However, there are existing limitations that must be addressed in future research. First, we model patient transfers that heavily rely on the proper functioning of the transportation system during the emergency response. However, our paper does not capture that the transportation network can be disrupted owing to potential bridge failures, seismic liquefaction, or infrastructure debris caused by the earthquake. Although there are models to capture these disruptions in a large city, we did not capture them because they require extensive seismic vulnerability data currently not available for Lima. Only a few large urban centers worldwide have sufficient vulnerability data to start capturing disruptions in the entire transportation network, e.g., the Bay Area in California50. Because collecting such data often requires significant resources from cities, strategic surveying of critical elements [e.g., critical bridges and roads] in the system can be an effective starting point for cities that lack sufficient vulnerability data. Our results can be used to support such a strategic surveying approach in large urban centers Instead of exhaustively collecting the vulnerability data of all components of the transportation network, the de facto approach in risk analysis, researchers can use our results to prioritize surveying the critical roads for patient transfers to evaluate its potential disruptions owing to structural failure, soil liquefaction, and debris blockage and propose strategic risk mitigation measures for the network. Similarly, the power, water, and sewage networks67 are pivotal for the proper functioning of the hospital facilitates. Our results can help future research focus on the power substations, power distribution lines, and water and sewage pipes serving the critical hospitals in the system. Focusing on these critical components will enable large urban centers which lack data to have a robust starting point for including the interactions between the hospital system and other critical urban systems.

Second, our case study only included an evaluation of an earthquake occurring at nighttime because we lacked data with the spatial distribution of the urban population at other times of the day. This spatial distribution is an important factor in the assessment of the spatial distributions of earthquake casualties because it enables researchers to track what vulnerable buildings are occupied. In our nighttime scenario, people are mostly at residential buildings, which are particularly vulnerable in Lima. We used LandScan information, which is available worldwide68, as a proxy for the nighttime distribution of the population16,17. Earthquake scenarios occurring during the daytime will have a different distribution of population and therefore a different spatial distribution of earthquake casualties. Although we were not able to track the time variations of urban population in Lima, existing work has already shown that mobile network data can be effectively used for it, e.g., Beijing in China69. As more mobility data are rapidly collected by public and private institutions, plenty of opportunities to create large databases with time-variant high-resolution urban densities will be available in the near future. Deployments of models to track these time-variant urban densities will enable researchers to leverage the formulation presented here and extend the emergency response application to different times of the day in multiple cities so that emergency managers are better informed on how to protect their communities.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Data availability

All the data to reproduce the findings of the paper can be found at //purl.stanford.edu/dp530wq8437. Source data for the figures presented in the paper are also provided in the same link.

Code availability

All the computer code to reproduce the findings of the paper can also be found at //purl.stanford.edu/dp530wq8437.

References

  1. Centre for Research on the Epidemiology of Disasters. EM-DAT The international disasters database //www.emdat.be/ [2019].

  2. Myrtle, R. C., Masri, S. F., Nigbor, R. L. & Caffrey, J. P. Classification and prioritization of essential systems in hospitals under extreme events. Earthq. Spectra 21, 779–802 [2005].

    Google Scholar 

  3. American Red Cross MultiDisciplinary Team. Report on the 2010 Chilean Earthquake and Tsunami Response: U.S. Geological Survey. Open-File Report 2011-1053 v1.1. [Virginia, 2011]. //pubs.usgs.gov/of/2011/1053/.

  4. Parmar, P., Arii, M. & Kayden, S. Learning from japan: strengthening US emergency care and disaster response. Health Aff. 32, 2172–2178 [2013].

    Google Scholar 

  5. Schultz, C., Koenig, K. & Lewis, R. Decisionmaking in hospital earthquake evacuation: does distance from the epicenter matter? Ann. Emerg. Med. 50, 320–326 [2007].

    PubMed  Google Scholar 

  6. Pan-American Health Organization [PAHO]—World Health Organization [WHO]. Resolution CD50.R15: Plan of Action of Safe Hospitals. In 50th Directory Council, 62nd Session of the Regional Committee [Washington, D.C., USA, 2010].

  7. World Health Organization. A Strategic Framewofk for Emergency Preparedness. [Geneva, Switzerland [2017]. //apps.who.int/iris/bitstream/10665/254883/1/9789241511827-eng.pdf.

  8. Cimellaro, G. P., Reinhorn, A. M. & Bruneau, M. Performance-based metamodel for healthcare facilities. Earthq. Eng. Struct. Dyn. 41, 1549–1568 [2011].

    Google Scholar 

  9. Yavari, S. et al. Modeling post-earthquake functionality of regional health care facilities. Earthq. Spectra 26, 869–892 [2010].

    Google Scholar 

  10. Jacques, C. C. et al. Resilience of the canterbury hospital system to the 2011 Christchurch earthquake. Earthq. Spectra 30, 533–554 [2014].

    Google Scholar 

  11. Tarque, N., et al. Basic seismic response capability of hospitals in Lima, Peru. Disaster Med. Public Health Prep. 13, 138–143 [2018].

  12. Yi, P., George, S. K., Paul, J. A. & Lin, L. Hospital capacity planning for disaster emergency management. Socio-Economic Plan. Sci. 44, 151–160 [2010].

    Google Scholar 

  13. Gul, M. & Guneri, A. F. A comprehensive review of emergency department simulation applications for normal and disaster conditions. Computers Ind. Eng. 83, 327–344 [2015].

    Google Scholar 

  14. Vugrin, E. et al. Modeling hospitals’ adaptive capacity during a loss of infrastructure services. J. Healthc. Eng. 6, 85–120 [2015].

    PubMed  Google Scholar 

  15. Aghapour, A. H., Yazdani, M., Jolai, F. & Mojtahedi, M. Capacity planning and reconfiguration for disaster-resilient health infrastructure. J. Build. Eng. 26, 100853 [2019].

    Google Scholar 

  16. Ceferino, L., Kiremidjian, A. & Deierlein, G., Regional multi-severity casualty estimation due to building damage following a mw 8.8 earthquake scenario in Lima, Peru. Earthq. Spectra 34, 1739–1761 [2018].

  17. Ceferino, L., Kiremidjian, A. S. & Deierlein, G. G. Probabilistic model for regional multi-severity casualty estimation due to building damage following an earthquake. ASCE-ASME J. Risk Uncert. Eng. Syst Part A: Civ. Eng. 4 [2018].

  18. Santa Cruz, S., Blondet, M., Muñoz, A., Palomino Bendezú, J. & Tamayo, R. Evaluación Probabilistica de riesgo Sísmico de Escuelas y Hospitales de la ciudad de Lima. Componente 2: Evaluación Probabilística del Riesgo Sísmico de Hospitales en la ciudad de Lima. [Peru, 2013].

  19. Liguori, N. et al. Hospital treatment capacity in case of seismic scenario in the Lima Metropolitan area, Peru. Int. J. Disaster Risk Reduct. 38, 101196 [2019].

    Google Scholar 

  20. World Health Organization [WHO]. Minimum Technical Standards and Recommendations for Rehabilitation–Emergency Medical Teams. [Geneva, 2016] //apps.who.int/iris/handle/10665/252809.

  21. Ceferino, L., Kiremidjian, A. & Deierlein, G. Probabilistic Space and Time Interaction Modeling of Mainshock Earthquake Rupture Occurrence.Bull. Seismol. Soc. Am. //doi.org/10.1785/0120180220 [2020].

  22. Silgado, E. Historia de los Sismos más notables en el Perú, 1513-1974. Instituto Geológico Minero131 [1978].

  23. Kelleher, Ja. Rupture zones of large South American earthquakes and some predictions. J. Geophys. Res. 77, 2087 [1972].

    ADS  Google Scholar 

  24. Naghi, T. et al. Musculoskeletal injuries associated with earthquake: a report of injuries of Iran’s December 26, 2003 Bam earthquake casualties managed in tertiary referral centers. Injury 36, 27–32 [2005].

    Google Scholar 

  25. Li, W. et al. Management of severe crush injury in a front-line tent ICU after the 2008 Wenchuan earthquake in China: an experience with 32 cases. Crit. Care 13, R178 [2009].

    PubMed  PubMed Central  Google Scholar 

  26. Zavala, C., Honma, C., Gibu, P., Gallardo, J. & Huaco, G. Full Scale on Line Test on Two Story Masonry Building Using Handmade Bricks. 13th World Conference on Earthquake Engineering. Paper no. 2885 [Vancouver, 2004].

  27. Quiroz, L. G., Maruyama, Y. & Zavala, C. Cyclic behavior of Peruvian confined masonry walls and calibration of numerical model using genetic algorithms. Eng. Struct. 75, 561–576 [2014].

    Google Scholar 

  28. Bambarén, C. Legal issues of humanitarian assistance after the 2007 earthquake in Pisco, Peru. Prehosp. Disaster Med. 25, 203–206 [2010].

    PubMed  Google Scholar 

  29. Oraganización Panamericana de la Salud–Organización Mundial de la Salud. Guía del evaluador Hospitales seguros frente a desastres. Segunda edición [Washington, DC, 2008].

  30. Pretto, E. A. et al. An analysis of prehospital mortality in an earthquake. Disaster Reanimatology Study Group. Prehosp. Disaster Med. 9, 107–117 [1994].

    CAS  PubMed  Google Scholar 

  31. Paul, J. A. & Lin, L. Impact of facility damages on hospital capacities for decision support in disaster response planning for an earthquake. Prehosp. Disaster Med. 24, 333–341 [2009].

    PubMed  Google Scholar 

  32. Pretto, E. A. et al. Disaster reanimatology potentials: a structured interview study in armenia. iii. results, conclusions, and recommendations. Prehosp. Disaster Med. 7, 327–337 [1992].

    Google Scholar 

  33. Malish, R. et al. Potential roles of military-specific response to natural disasters—analysis of the rapid deployment of a mobile surgical team to the 2007 peruvian earthquake. Prehosp. Disaster Med. 24, 3–8 [2009].

    PubMed  Google Scholar 

  34. Li, X.-H. & Zheng, J.-C. Efficient post-disaster patient transportation and transfer: experiences and lessons learned in emergency medical rescue in Aceh after the 2004 Asian tsunami. Mil. Med. 179, 913–9 [2014].

    PubMed  Google Scholar 

  35. Ardagh, M. W. et al. The initial health-system response to the earthquake in Christchurch, New Zealand, in February, 2011. Lancet 379, 2109–2115 [2012].

    PubMed  Google Scholar 

  36. Awais, S. & Saeed, A. Study of the severity of musculoskeletal injuries and triage during the 2005 Pakistan earthquake. Int. Orthop. 37, 1443–1447 [2013].

    PubMed  PubMed Central  Google Scholar 

  37. Wang, C. et al. Evacuation burden of a safety-net academic medical center during hurricane sandy: implications for reverse triage. Prehosp. Disaster Med. 32, S125–S126 [2017].

    Google Scholar 

  38. Córdova-Aguilar, H. la periferia de Lima Metropolitana frente al cambio climático. Reconociendo las geografías de América Latina y el Caribe. 209–232 [2017].

  39. Instituto Nacional de Estadística e Informática—INEI. Planos Estratificados de Lima Metropolitana a Nivel de Manzana 2016 según ingreso per cápita del hogar y según grupos de pobreza monetaria. Tech. Rep. [Lima, 2016].

  40. Bitrán, R., Giedion, U., Valenzuela, R. & Monkkonen, P. Keeping Healthy in an Urban Environment: Public Health Challenges for the Urban Poor. In Fay, M. [ed.] The Urban Poor in Latin America, chapter 3, 179–194 [The World Bank, Washington, D.C., 2005].

  41. Global Facility for Disaster Reduction and Recovery [GFDRR]—World Bank. Disaster Risk Management in Latin America and the Caribbean Region: GFDRR Country Notes. Washington, D.C.: World Bank Group [2012].

  42. Stratton, S. J. et al. The 1994 Northridge earthquake disaster response: the local emergency medical services agency experience. Prehosp. Disaster Med. 11, 172–179 [1996].

    CAS  PubMed  Google Scholar 

  43. Dolan, B., Esson, A., Grainger, P. P., Richardson, S. & Ardagh, M. Earthquake disaster response in christchurch, New Zealand. J. Emerg. Nurs. 37, 506–9 [2011].

    PubMed  Google Scholar 

  44. Zhang, L. et al. Emergency medical rescue efforts after a major earthquake: lessons from the 2008 Wenchuan earthquake. Lancet 379, 853–861 [2012].

    PubMed  Google Scholar 

  45. Bar-Dayan, Y. et al. An earthquake disaster in Turkey: an overview of the experience of the Israeli Defence Forces field hospital in Adapazari. Disasters 24, 262–270 [2000].

    CAS  PubMed  Google Scholar 

  46. Lee, V. J., Low, E., Ng, Y. Y. & Teo, C. Disaster relief and initial response to the earthquake and tsunami in Meulaboh, Indonesia. Ann. Acad. Med. Singap. 34, 586–590 [2005].

    CAS  PubMed  Google Scholar 

  47. Ouyang, M., Dueñas-Osorio, L. & Min, X. A three-stage resilience analysis framework for urban infrastructure systems. Struct. Saf. 36-37, 23–31 [2012].

    Google Scholar 

  48. Fonoberova, M., Algorithms for Finding Optimal Flows in Dynamic Networks. In Rebennack, S., Pardalos, P. M., Pereira, M. V. F. & Iliadis, N. A. [eds.] Handbook of Power Systems II, chap. 2 [Springer, 2010].

  49. Nasrabadi, E. & Hashemi, S. M. Minimum cost time-varying network flow problems. Optim. Methods Softw. 25, 429–447 [2010].

    MathSciNet  MATH  Google Scholar 

  50. Miller, M. & Baker, J. W. Coupling mode-destination accessibility with seismic risk assessment to identify at-risk communities. Reliab. Eng. Syst. Saf. 147, 60–71 [2016].

    Google Scholar 

  51. von Schreeb, J., Louis, R., Hans, S. & Hans, R. Foreign field hospitals in the recent sudden-onset disasters in Iran, Haiti, Indonesia, and Pakistan. Prehosp. Disaster Med. 23, 144–151 [2008].

    Google Scholar 

  52. Andersen, M. S., Dahl, J. & Vandenberghe, L., CVXOPT: A Python package for convex optimization, version 1.2 abel.ee.ucla.edu/cvxopt [2018].

  53. Villar-Vega, M. et al. Development of a fragility model for the residential building stock in South America. Earthq. Spectra 33, 010716EQS005M [2017].

    Google Scholar 

  54. Calderon, D. Dynamic Characteristics of the Soils in Lima, Peru, by estimating Shallow and Deep Shear-wave Velocity Profiles. Ph.D. thesis [2012].

  55. Jaiswal, K., Wald, D. J. & Hearne, M. G. Estimating casualties for large earthquakes worldwide using an empirical approach. Earthq. Spectra 29, //doi.org/10.1193/1.4000104 [2009].

  56. Noh, H. Y., Kiremidjian, A., Ceferino, L. & So, E. Bayesian updating of earthquake vulnerability functions with application to mortality rates. Earthq. Spectra 33, 1173–1189 [2017].

    Google Scholar 

  57. Federal Emergency Management Agency [FEMA]. Multi-hazard Loss Estimation Methodology: Earthquake Model. Hazus®-MH 2.1: Technical Manual. [2015].

  58. Ceferino, L., Kiremidjian, A. & Deierlein, G., Computing Hospital System Resilience: a Supply-Demand Perspective. In 11th National Conference on Earthquake Engineering [NCEE] [Los Angeles, 2018].

  59. Mitrani-Reiser, J. et al. A functional loss assessment of a hospital system in the Bío-Bío province. Earthq. Spectra 28, 473–502 [2012].

    Google Scholar 

  60. Kirsch, T. D. et al. Impact on hospital functions following the 2010 Chilean earthquake. Disaster Med. Public Health Prep. 4, 122–128 [2010].

    PubMed  Google Scholar 

  61. Dirección General de Gestión del Desarrollo de Recursos Humanos. Recursos Humanos en Salud al 2011. Evidencia de Toma de Decisiones. Lima: Ministerio de Salud. OPS peru, 1126 [2011].

  62. Jumpa, M., Jan, S. & Mills, A. The role of regulation in influencing income-generating activities among public sector doctors in Peru. Hum. Resour. Health 5, 1–8 [2007].

    Google Scholar 

  63. Strasser, F. O., Arango, M. & Bommer, J. J. Scaling of the source dimensions of interface and intraslab subduction-zone earthquakes with moment magnitude. Seismol. Res. Lett. 81, 951–954 [2010].

    Google Scholar 

  64. Abrahamson, N., Gregor, N. & Addo, K. BC hydro ground motion prediction equations for subduction earthquakes. Earthq. Spectra 32, 23–44 [2016].

    Google Scholar 

  65. Goda, K. & Atkinson, G. M. Probabilistic characterization of spatially correlated response spectra for earthquakes in Japan. Bull. Seismol. Soc. Am. 99, 3003–3020 [2009].

    Google Scholar 

  66. Markhvida, M., Ceferino, L. & Baker, J. W., Modeling spatially correlated spectral accelerations at multiple periods using principal component analysis and geostatistics. Earthq. Eng. Struct. D. 47, 1107–1123 [2018].

  67. United States Geological Survey. The HayWired Earthquake Scenario–Engineering Implications Scientific Investigations. Report 2017-5013-I-Q. [2017].

  68. Oak Ridge National Laboratory & East View Cartographic, I. East View LandScan global 2012 [2013].

  69. Wang, Z. et al. Monitoring disaster-related power outages using nasa black marble nighttime light product. ISPRS–Int. Arch. Photogramm., Remote Sens. Spat. Inf. Sci. XLII-3, 1853–1856 [2018].

    Google Scholar 

  70. Dorbath, L., Cisternas, A. & Dorbath, C. Assessment of the size of large and great historical earthquakes in Peru. Bull. Seismol. Soc. Am. 80, 551–576 [1990].

    Google Scholar 

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Acknowledgements

We thank Dr. Maryia Markhvida, Abhinav Bindal, and Jacqueline Li for helping conceptualize the first version of the patient transfer analysis during an emergency response. We also thank professor Sandra Santa Cruz, from the Pontificia Universidad Católica del Perú for granting access to the hospitals’ seismic vulnerability information, and professor Carlos Zavala and Miguel Estrada from the Centro Peruano-Japonés de Investigaciones Sísmicas y Mitigación de Desastres [CISMID] and the Universidad Nacional de Ingeniería [UNI] for providing access to the seismic microzonation data in Lima. We thank Dr. Ken Snyder, Dr. Juan Fung, and Dr. Siamak Sattar from NIST for providing valuable feedback for our paper and Jill O’Nan from Stanford University for helpful revision of the paper writing. We acknowledge the financial support by the John A. Blume Fellowship from the Civil Engineering Department at Stanford University. In addition, this research was partially supported by the NSF Grant 1645335. The authors are grateful for their generous support.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, USA

    Luis Ceferino, Anne Kiremidjian & Gregory Deierlein

  2. The Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ, USA

    Luis Ceferino

  3. Materials and Structural Systems Division, Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA

    Judith Mitrani-Reiser

  4. School of Public Health and Administration, Universidad Peruana Cayetano Heredia, Lima, Peru

    Celso Bambarén

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  1. Luis Ceferino

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  2. Judith Mitrani-Reiser

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  3. Anne Kiremidjian

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  4. Gregory Deierlein

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  5. Celso Bambarén

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Contributions

L.C., A.K., and G.D. conceived the basic emergency response network model, curated the data to model post-earthquake hospital functionality and set up the earthquake casualty model. L.C., J.M., A.K, and G.D. reviewed and refined the hospital functionality model to focus on high-severity injuries and defined the metrics to measure the effectiveness of emergency response plans. L.C., J.M., and C.B. defined the strategies for emergency response included in the paper. C.B. provided further guidance on the modeling of the deployment of EMTs and ambulance sharing. L.C. drafted the manuscript with contributions and editing from all the authors.

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Correspondence to Luis Ceferino.

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Ceferino, L., Mitrani-Reiser, J., Kiremidjian, A. et al. Effective plans for hospital system response to earthquake emergencies. Nat Commun 11, 4325 [2020]. //doi.org/10.1038/s41467-020-18072-w

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  • Received: 20 September 2019

  • Accepted: 27 July 2020

  • Published: 28 August 2020

  • DOI: //doi.org/10.1038/s41467-020-18072-w

What is disaster preparedness and response?

Disaster preparedness consists of a set of measures undertaken in advance by governments, organisations, communities, or individuals to better respond and cope with the immediate aftermath of a disaster, whether it be human-induced or caused by natural hazards.

What are the approaches toward disaster management?

Preparation , Mitigation, Rescue & Relief, and Rehabilitation are the main phases in a disaster management . Identification of the existing policies and facilities in the state has an important role .

What is a proactive approach to disasters?

This might be through: prevention efforts prior to, and preparedness for, emergencies; reduction of further exposure and suffering during emergencies; and building the mental health system back better following emergencies and in preparation for future events.

What are the 3 basic strategies of disaster response?

[1] Reduce, or avoid, losses from hazards; [2] Assure prompt assistance to victims; [3] Achieve rapid and effective recovery.

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