Classic Data-Dependent Decision-Making Theories for Public Health Emergencies

To upgrade the emergency response efficiency of the emergency department (ED), scholars have exerted expansive research effort on the hospital surge capacity and patient flow determinants. McCarthy and his team have reviewed daily ED surges and the ED surge capacity and illustrated this indicator’s potential relevance during a catastrophic event. The team proposed that daily and catastrophic ED surges can be measured by the magnitude of the surge, as well as the nature and severity of the illnesses and injuries that patients present during the surge. The results help increase the understanding of the daily ED surge capacity and influencing factors. This information then improves the ability to simulate the potential impact of different types of catastrophic events on the surge capacity of hospital EDs nationwide.Reference McCarthy, Aronsky and Kelen⁵ Afterward, the scholars developed a methodology for predicting the demand for ED services by using the regression model. The findings showed that the medical demand for ED services was well approximated by the Poisson regression model.Reference McCarthy, Zeger and Ding⁶ Furthermore, the effect of ED crowding on clinical outcomes has been studied and evaluated by scholars, such as Steven and Dominik.Reference Bernstein, Aronsky and Duseja⁷ Their studies revealed that ED crowding is associated with objective clinical endpoints, such as mortality, as well as clinically important processes of care.Reference Bernstein, Aronsky and Duseja⁷ By observational study, Forster and colleaguesReference Forster, Stiell and Wells⁸ investigated the effect of hospital occupancy on ED length of stay and patient disposition by using administrative data from a 500-bed acute care teaching hospital. Their precise research result showed that increased hospital occupancy is strongly associated with ED length of stay for admitted patients, and increasing the hospital bed availability might reduce ED overcrowding.Reference Forster, Stiell and Wells⁸

The previous works provide theory and technique foundation for building further accurate prediction and response models for public health emergencies. However, most of these models are strongly dependent on historical data. By contrast, when a complex and unrepeatable unconventional public health emergency, such as the SARS outbreak in 2003, is faced without sufficient data and experience, the models become inapplicable and unreliable. Moreover, given only classical theories, we often lack sufficient prior knowledge on how to describe emergency scenarios accurately and even analyze and optimize the public health response systems effectively and dynamically.

Simulation of Decision-Making Methods for Emergency Response

Given the emergency response problems, simulation methods (especially the models described in mathematical form) are studied and applied abroad. On the basis of Petri Net simulation technology, with oil can fire as an example, the performance of the China urban emergency response system and response plan are analyzed.Reference Zhong, Shi and Fu^9, Reference Zhou¹⁰ When examining the panic features of people escaping from disaster, simulations based on a model of pedestrian behavior are available.Reference Helbing, Farkas and Vicsek¹¹ Meanwhile, a 2D finite volume method is used to simulate the dam-break process with a case.Reference Valiani, Caleffi and Zanni¹²

The models proposed in the previous studies demonstrated that simulation decision-making methods are useful for certain kinds of emergencies. However, on the one hand, most current simulation models are designed for industrial disaster scenarios with no clear confirmation of successful application to unconventional public health emergencies. On the other hand, the models mainly focus on emergencies and the relevant response processes with features, such as short span of time and space and clear mechanism. With sufficient theoretical basis (former models or knowledge), the simulation decision models are constructible.Reference Ni, Rong and Wang^13, Reference Bo-Hu, Chai and Hou¹⁴ However, for complex, dynamic, and uncertain unconventional public health emergencies, no sufficient prior knowledge is available to support the traditional simulation modeling process. Therefore, new evolutionary and dynamical simulation decision-making methods should emerge as necessary.

Parallel Simulation-Based, Scenario–Response Emergency Management Paradigm

In the new information and communication technology era, the processes of perception, computing, storage, transmitting, and analysis have achieved great performance improvements with the technologies of cloud computing and Internet of Things. In the aspect of simulation platform, the networked modeling and simulation platform based on cloud computing, named cloud simulation platform, is proposed for complex cross-domain system analysis and improvement. Theoretically, in such a high-performance technology environment, complex disaster scenarios and emergency response processes can be shown in simulation platform dynamically and interactively. Moreover, the promising scenario–response emergency decision-making paradigm based on theories of artificial society modeling and parallel emergency management is proposed by the researchers of the Chinese Academy of Sciences and National University of Defense Technology for unconventional disaster scenario simulation and comprehensive analysis, emergency resource scheduling, and evacuations.Reference Yang, Yang, Jin and Lin^2, Reference Wang¹⁵

Unlike the data-dependent prediction–response emergency decision-making paradigm based on statistical regression and numerical calculation, the structure-dependent scenario–response paradigm is based on bottom-up modeling methods. This paradigm can help decision makers dynamically simulate artificial society and disaster scenarios that increasingly approximate real-world scenarios through parallel individual and interactive relationship modeling under a first-time disaster, which hence lacks historical data and experience.Reference Wang, Qiu and Zeng⁴ Scholars adopted the SARS outbreak as an example and used the multi-agent simulation method to study and discover the evolution mechanism of an unconventional public health emergency.Reference Zhong, Mao and Weng¹ However, given the great difficulty in modeling and the high cost in calculating, the promising “heavyweight” parallel simulation technologies remain in the idealized experimental research stage.

Discrete Event System Theory

Discrete event system (DES) is an event-driven dynamic system with internal states that change from one to another randomly. The DES theory has been applied as a means to analyze health care systems. The main research work includes applying this theory to health care processes, analyzing the effect of patient arrival and service time variability on patient waiting time and throughput and examining the efficiency of dedicated (specialized) and combined resources.Reference Kolker and Rodrigues¹⁶ DES-based simulation has become a popular and effective decision-making tool for the optimal allocation of scarce health care resources to improve patient flow while minimizing health care delivery costs and increasing patient satisfaction. Combined optimization and simulation tools also allow decision makers to quickly determine optimal system configurations, even for complex integrated health care systems (eg, hospitals, outpatient clinics, EDs, and pharmacies).Reference Jacobson, Hall and Swisher¹⁷

The previously mentioned works have not demonstrated the successful application of DES theory in unconventional public health emergencies but show that the theory can model public health system structures and effectively simulate these structures’ processes. Actually, the formation processes of emergency demand (such as patient arrivals), response capacities (such as medical service rates), and the variation rates of response system states constantly exhibit strong randomness. In this regard, in special society systems, unconventional emergency response systems can be described by the DES theory properly. At present, the DES theory is available for combining with object-oriented (OO) modeling and simulation technology (such as FlexSim, Arena, Petri Net). On the basis of this technology, system elements, relationships, layouts, response processes, and some other uncertainties (such as the previously mentioned statistical regularities) of real systems can be quickly transformed into simulation models for making emergency response decisions effectively.Reference Budgaga, Malensek and Pallickara^18, Reference Furian, O’sullivan and Walker¹⁹

Inspired by the DES theory, unconventional public health emergency scenarios and hospital surge capacities can be considered as a whole scenario–response system. Then, by modeling and simulation based on DES, effective decision-making processes, such as scenario anticipation and medical resource allocation and hospital surge capacity optimization, can be achieved and improved.

Lightweight DES-Based Parallel Simulation Decision-Making Framework (DES–PSDF)

The parallel emergency management theory proposes that real disasters can be predicted accurately. However, on the basis of the experimental simulation environment, we can build artificial society models that parallel with real-world scenarios. Then, with the real-time data collected from real scenarios, the models can be updated and improved dynamically, and the evolution processes can be shown in the models. Through the parallel artificial society simulation model, functions, such as scenario analysis and prediction, response solution brainstorming and optimization, can be conducted to support emergency response decision-making processes. Therefore, the lightweight DES–PSDF for emergency response is proposed in this section. The structure of this framework consists of a real scenario layer and a simulation decision-making layer that are parallel to each other (Figure 1).

FIGURE 1

Lightweight Discrete Event System-Based Parallel Simulation Decision-Making Framework (DES-PSDF).

Abstract Structure Modeling

On the basis of the DES theory and OO modeling methods, the DES–ASDM can be constructed from the perspectives of entity, attribute, and relationship flow.Reference Budgaga, Malensek and Pallickara^18, Reference Furian, O’sullivan and Walker¹⁹ The base structure of the model can be described as the triple DES–ASDM::={E,A,F}. That is, an entity (E) set with its attribute (A) set and its relationship flow (F) set. Two kinds of entity classes, including temporary entity (TE) and permanent entity (PE), are basic elements of simulation models. As an execution subject of emergency RPs, the PE does not leave the models until the simulation ends. The performances and states are usually stable and do not change with the simulations. On the contrary, as the supporting objects, TEs are processed or recurrent in emergency response, and their states usually change with the simulation processes. Furthermore, the important features of entities, including the type, function, state, and statistical distribution, are described into the set A of attributes. The relationships flow set F is used for representing the directed interconnections between entities. Concurrently, the input–output relationships of the RPs, which are the basic units for achieving the emergency response systems and their RPs, are also described by the directed flows (Figure 2).

FIGURE 2

DES–ASDM for Unconventional Public Health Emergencies.

The DES–ASDM for emergency medical response is defined with 5 kinds of elements, including the AB, EmD, RP, RO, and RR. If the pe (element of PE), te (element of TE), f (element of F), and attribute (element of A) are represented with a rectangle, circle, arrow and text box, respectively, under an emergency medical RP, as an example, the resultant abstract simulation model is as shown in Figure 2.

Defining the Simulation Entities and Their Attributes

Because emergency ROs are constantly executing RPs with stable performances in emergency systems, the former are classic PEs. For example, as an emergency response subject, every medical staff member diagnoses or cures patients repeatedly with a stable service rate (number of patients cured per hour) during a running simulation. The staff member does not leave the simulation system until the simulation ends. Therefore, the ROs can be defined into the PEs (PE_RO), that is, $RO\buildrel {Map} \over \longrightarrow P{E_{RO}}$, where $RO = \{ r{o_1},r{o_2},...\}$ means the set of ROs and $PE = \{ p{e_{RO1}},p{e_{RO2}},...\}$ means the set of PEs. Usually, because every ro performs one response activity, the element also directly represents a response activity.

Because ABs and RRs are changing and passive objects in RPs, the former two elements should be transformed into TEs (TE_AB and TE_RR, respectively) of the simulation models, that is, $AB\buildrel {Map} \over \longrightarrow T{E_{AB}}$, where $AB = \{ a{b_1},a{b_2},...\}$ means the set of ABs and $TE = \{ t{e_{AB1}},t{e_{AB2}},...\}$ means the set of relevant TEs.

Similarly, the RRs are defined into the TEs, that is, $RR\buildrel {Map} \over \longrightarrow T{E_{RR}}$, where $RR = \{ r{r_1},r{r_2},...\}$ means set of RRs and $TE = \{ t{e_{RR1}},t{e_{RR2}},...\}$ means set of relevant TEs.

Therefore, for one entity e_i, the attributes and attribute types are defined as follows:

$$\eqalign{ Attribut{e_i} = \{ a{t_{i1}},a{t_{i2}},...,a{t_{im}}\} \buildrel {Map} \over \longrightarrow \sum\nolimits_{{e_i}} { = \{ {a_{i1}}} ,{a_{i2}},...,{a_{im}}\} \cr \forall Type(a{t_{ij}})\buildrel {Map} \over \longrightarrow Type({a_{ij}}) \cr} $$

where at_ij denotes the attribute type j of the entity e_i, a_ji denotes the set of its attribute values, and the symbol$\sum\nolimits $here means all of the attribute types of entity e_i. For example, the PEs can serve as response units, such as doctors and nurses, and their attributes can include the name, vocation, state, and performance. If the TEs are ABs, such as patients, equipment, and buildings, the TEs’ relevant attributes include the destruction degree, injury or illness degree, and location. If the TEs are RRs, such as food and medicine, the TEs’ relevant attributes should include name, quantity, and price.

Defining the Relationship Flows Between Entities

After identifying the input–output–precondition–effect relationships between pairs of TE and PE in accordance with the RPs, the directed flows can be defined between the PEs. Two kinds of flows exist and include the response process flow (RPF) and response support flow (RSF). For example, patients enter the medical response system individually or simultaneously under certain rules or DES random distribution (Figure 2). Then, this process can be described into a directed entity relationship flow f_DS-RO1 and means that the TEte_ABi (patient i) flows from the PEpe_DS (source of disease outbreak) to the PEpe_RO1 (first RP, such as queuing or waiting for diagnosis). Similarly, after diagnosing with the support of pe_RR1 (diagnostic tools or medicines), the te_ABi flows from the PEpe_RO1 to the PE pe_RO2 (second RP, such as treatment), and this process is represented in the flow as f_RO1-RO2. Then, the previously mentioned serial forward processes can be described into the RPF set F_Process = {f_DS-RO1,f_RO1-RO2,…,f_RO2-RO3}. Besides, as emergency RRs, medicines are consumed to support the RPs. The relevant directed relationship flows are described into the RSF set F_Support = {f_RR1-RO1,f_RR2-RO2,…}. Therefore, the general entity relationship flow can be defined as follows:

$$F = \{ t{e_k},{a_{tek}},w, \lt p{e_i},p{e_j} \gt |t{e_k} \in TE,{a_{tek}} \in {A_{tek}},w \in W, \lt p{e_i},p{e_j} \gt \in PE \times PE\} $$

where te_k denotes the TEs in the flows, a_tek denotes the attribute values of the entities, <pe_i, pe_j> denotes the ordered pairs where the TE flows from the pe_i to pe_j, and w is a weight variable used for describing the input or output constraints to trigger the actions performed by pe_RO (RO). If w_i denotes the output constraints of pe_ROi and w_j denotes the input constraints of pe_ROj, the flow can be represented as shown below:

$${\rm{t}}{{\rm{e}}_{\rm{k}}} \in ^\circ\,\!{\rm{p}}{{\rm{e}}_{\rm{j}}}\,\!\cap \,\!{\rm{t}}{{\rm{e}}_{\rm{k}}} \in {\rm{p}}{{\rm{e}}_{\rm{i}}}^\circ ,\;\;\;{{\rm{A}}_{{\rm{tek}}}}\;\ge \,\!{{\rm{W}}_{\rm{j}}}\,\!\cap \,\!{{\rm{A}}_{{\rm{tek}}}}\;\le \,\!{{\rm{W}}_{\rm{i}}}$$

This relation means that if f is the output flow of the RO (activity) pe_i, then the relevant attribute values of the TEs must be less than or equal to the output weight, similar to the number of evacuees that must be below the capacity of the shelter. If f is the input flow of the RO pe_j, then the relevant attribute values of the TEs must be greater than or equal to the input weight, similar to the necessary medicine inputting when accomplishing medical response activities.

Simulation Operation and Decision-Making Optimization

Designing and Achieving Initial Simulation Models

As a common modeling paradigm, the DES–ASDM shows the structures, situations, and activities of real disaster scenarios at the abstract mechanism level. Actually, some OO or visualization simulation tools, such as FlexSim, Arena, and CPN Tools, are based on DES theory.Reference Lavery, Beaverstock and Greenwood^22–Reference Pokraev²⁴ Therefore, to render the methods proposed in this paper further realizable, we must design compatible and extensible, relevant transformation principles from the elements of the DES–ASDM to the elements of the simulation software. With the transformation principles, the abstract simulation and decision-making models with the relevant functions, such as parameter computing, statistical analysis, and presenting, can be achieved effectively for the emergency response simulation and decision-making processes.

If the abstract simulation model is achieved with the FlexSim tool, the transforming principles are shown in Table 1. First, as the emergency response objects processed by the relevant subjects in the real scenarios, the affected bodies and RRs are described as the temporary entities TE_AB and TE_RR, respectively, in the abstract models. Then, the FlowItem components such as Box or Person are loaded to achieve the functions of the previously mentioned 2 temporary entities with the FlexSim tools. Second, the emergency response subjects are described as permanent entities, such as organizations and equipments are defined as PE_RO and PE_RE, respectively. Then, the Fixed Resource or Task Executers components, such as Processor/Operator and Transporter can be used for achieving the relevant functions of them with the FlexSim tools. By setting the parameters of the components, the response modes and performances can be adjusted. Third, the emergency RPs of real scenarios are described as RP flows and RSFs, which can be achieved by loading the Connect Object and Travel Network functions in FlexSim. Finally, the emergency demand of real scenarios, such as the number and the arrival rate of patients, is defined as permanent entities. Then, with the relevant parameters setting, the Source component is loaded for simulating the function of events triggering.

TABLE 1

The Transformation Principles of “From Real Scenario to DES-ASDM to FlexSim”

According to the scenario, after achieving the structure and dynamic flows of the simulation model by loading the components of FlexSim, the initial data and the evolution rules can be obtained with the technologies of radio-frequency identification and distribution fitting software such as ExpertFit, and so on.Reference Fang, Qu and Li^25, Reference Kumar, McCreary and Nottestad²⁶ Then, by inputting the entity attribute values as parameters into the components, the initial simulation model can be achieved and optimized with FlexSim.

Parallel Control

Most often, emergencies, especially unconventional emergencies, have no historical precedent. Although the types of emergencies are the same as those that have occurred, the disaster-causing factors and evolution processes vary. Therefore, for every unconventional emergency, the evolution mechanism and emergency response demand are neither clear nor certain. Obtaining the accurate parameters of prediction models quickly is difficult under traditional management, and controlling theories are unable to describe, predict, and decide effectively during emergencies. Parallel controlling is the key idea of parallel emergency management theory. This process ensures the accuracy and dependability of decision-making results; simulation models must be dynamically developed and improved by keeping artificial scenarios synchronized with real scenarios.Reference Wang¹⁵

The parallel controlling principles are shown in Figure 3. When a new disaster Scenario 0 occurs, the parallel simulation system enters the response state immediately. First, by semantic matching with the scenarios of the existing model library,Reference Wang, Kang and Zhou^30, Reference Wang, Wong and Wang³¹ the decision makers should determine whether Scenario 0 involves previous situations. If a similar scenario exists, the relevant simulation model is the initial model, Model 0. Meanwhile, if no similar scenario exists in accordance with the current disaster scenario and response system situation, the initial simulation model, Model 0, can be constructed by the methods of data collecting and parameter fitting. Second, by steady simulation running data, the disaster evolution processes and the response effectiveness in future time will be projected. By observing or analyzing statistical data simulation results, we find the bottlenecks for proposing and implementing the improved response solutions. Concurrently, on the basis of a specific time–interval ▵t, the perceived information of real scenarios (from Scenario 1 to Scenario n) of the various stages of emergency RPs should be collected, integrated, and analyzed to synchronously modify the simulation models. By modifying processes, such as parameter refitting and data updating, the simulation models (from Model 1 to Model n) are continually improved to ensure that the simulation results are consistent with real scenarios in parallel evolution processes. Finally, when the whole emergency RP ends, the latest parameters and structure of the simulation model are recorded and archived in the model library for the next similar disasters.

FIGURE 3

Parallel Controlling Principles of the DES–ASDM for Emergency Response Simulation and Decision-Making Processes.