전염병 구획 모형에 대한 시스템다이내믹스 접근법: 국내 MERS 전염 SEIR 모형의 해석 및 변환 System Dynamics Approach to Epidemic Compartment Model: Translating SEIR Model for MERS Transmission in South Korea원문보기
수학모형의 한 유형인 구획모형은 전염병의 확산처럼 순차적인 이벤트나 프로세스로 구성된 동적 시스템의 변화를 분석하는 데 폭넓게 활용되어 왔다. 구획모형은 상자와 화살표로 표현되는 구획과 구획 간 관계로 구성된다. 이러한 원리는 stock과 flow로 구성되는 시스템다이내믹스(SD)의 모델링 원리와 비슷하다. 두 모형 모두 미분방정식을 이용하여 구조화된다. 이와 같은 두 모형 간 변환 가능성을 이용하여 국내 MERS 전염의 특징을 분석한 최근 연구의 SEIR 참조모형을 SD 관점에서 해석 변환한다. 변환된 SEIR 모형(Model 2)은 참조모형(Model 1)의 재현 결과와 비교하여 동일한 시뮬레이션 결과를 나타내었다. 본 연구는 전염병 구획모형의 구축에 도식과 미분방정식을 이용한 SD 방법론의 활용에 대한 인사이트를 제공하며, 변환된 SD 모형은 다른 전염병을 위한 참조모형으로 활용 가능하다.
수학모형의 한 유형인 구획모형은 전염병의 확산처럼 순차적인 이벤트나 프로세스로 구성된 동적 시스템의 변화를 분석하는 데 폭넓게 활용되어 왔다. 구획모형은 상자와 화살표로 표현되는 구획과 구획 간 관계로 구성된다. 이러한 원리는 stock과 flow로 구성되는 시스템다이내믹스(SD)의 모델링 원리와 비슷하다. 두 모형 모두 미분방정식을 이용하여 구조화된다. 이와 같은 두 모형 간 변환 가능성을 이용하여 국내 MERS 전염의 특징을 분석한 최근 연구의 SEIR 참조모형을 SD 관점에서 해석 변환한다. 변환된 SEIR 모형(Model 2)은 참조모형(Model 1)의 재현 결과와 비교하여 동일한 시뮬레이션 결과를 나타내었다. 본 연구는 전염병 구획모형의 구축에 도식과 미분방정식을 이용한 SD 방법론의 활용에 대한 인사이트를 제공하며, 변환된 SD 모형은 다른 전염병을 위한 참조모형으로 활용 가능하다.
Compartment models, a type of mathematical model, have been widely applied to characterize the changes in a dynamic system with sequential events or processes, such as the spread of an epidemic disease. A compartment model comprises compartments, and the relations between compartments are depicted a...
Compartment models, a type of mathematical model, have been widely applied to characterize the changes in a dynamic system with sequential events or processes, such as the spread of an epidemic disease. A compartment model comprises compartments, and the relations between compartments are depicted as boxes and arrows. This principle is similar to that of the system dynamics (SD) approach to constructing a simulation model with stocks and flows. In addition, both models are structured using differential equations. With this mutual and translatable principle, this study, in terms of SD, translates a reference SEIR model, which was developed in a recent study to characterize the transmission of the Middle East respiratory syndrome (MERS) in South Korea. Compared to the replicated result of the reference SEIR model (Model 1), the translated SEIR model (Model 2) demonstrates the same simulation result (error=0). The results of this study provide insight into the application of SD relative to constructing an epidemic compartment model using schematization and differential equations. The translated SD artifact can be used as a reference model for other epidemic diseases.
Compartment models, a type of mathematical model, have been widely applied to characterize the changes in a dynamic system with sequential events or processes, such as the spread of an epidemic disease. A compartment model comprises compartments, and the relations between compartments are depicted as boxes and arrows. This principle is similar to that of the system dynamics (SD) approach to constructing a simulation model with stocks and flows. In addition, both models are structured using differential equations. With this mutual and translatable principle, this study, in terms of SD, translates a reference SEIR model, which was developed in a recent study to characterize the transmission of the Middle East respiratory syndrome (MERS) in South Korea. Compared to the replicated result of the reference SEIR model (Model 1), the translated SEIR model (Model 2) demonstrates the same simulation result (error=0). The results of this study provide insight into the application of SD relative to constructing an epidemic compartment model using schematization and differential equations. The translated SD artifact can be used as a reference model for other epidemic diseases.
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문제 정의
This study aimed to translate an epidemic compartment model to an SD model using the sharable differential equations and schematic elements of compartment and SD simulation models. To facilitate procedural verification in terms of schematization and differential equations, this study employed the reference SEIR model produced by a recent study concerning MERS spread in South Korea.
제안 방법
Based on the findings shown in Fig. 2, this study constructed a discrete SEIR model for MERS transmission in South Korea using the Powersim Studio 8 software (See Fig. 3).
Based on the similarity between compartment and SD models, this study attempts to build an epidemic SEIR model using the SD approach by translating a discrete SEIR model into an SD model with sharable schematization and differential equations. To translate an epidemic compartment model, the discrete SEIR model proposed by Kwon and Jung [19] for a Middle East respiratory syndrome (MERS) outbreak in South Korea was used as a baseline model.
Based on this SEIR model and the clinical MERS data observed by the Korea CDC (See [19]; Table 1), the values of β, ϵ, and γ were estimated using the R programming language from May 20 to Oct 11, 2015, where the entire period was divided into three periods (Period 1, Period 2, and Period 3) relative to critical government action at T1 (disclosure of names of MERS-spread-hospitals) and T2 (closure of MERS-spread-hospitals).
However, in this study, a parameter estimation process was omitted to evaluate the translation accuracy of the SD approach from the reference SEIR model under the same environment. Thus, estimating the parameters of a compartment model in the SD approach will be addressed in a future study that will consider randomness for more extendable modeling of the SD approach.
This study aimed to translate an epidemic compartment model to an SD model using the sharable differential equations and schematic elements of compartment and SD simulation models. To facilitate procedural verification in terms of schematization and differential equations, this study employed the reference SEIR model produced by a recent study concerning MERS spread in South Korea. The translated SEIR model produced the same result as the replicated simulation result from the reference model.
To represent the reference SEIR model in SD, this study translated the four compartmental equations of S, E, I, and R to stocks and flows (in and out) for an SD model. Fig.
이론/모형
Based on the similarity between compartment and SD models, this study attempts to build an epidemic SEIR model using the SD approach by translating a discrete SEIR model into an SD model with sharable schematization and differential equations. To translate an epidemic compartment model, the discrete SEIR model proposed by Kwon and Jung [19] for a Middle East respiratory syndrome (MERS) outbreak in South Korea was used as a baseline model.
후속연구
However, in this study, a parameter estimation process was omitted to evaluate the translation accuracy of the SD approach from the reference SEIR model under the same environment. Thus, estimating the parameters of a compartment model in the SD approach will be addressed in a future study that will consider randomness for more extendable modeling of the SD approach.
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