학술논문
코로나19 확산 예측을 위한 네트워크 기반 모형 개발 / Development of a network-based model for predicting the spread of COVID-19
Document Type
Dissertation/ Thesis
Source
Subject
Language
Korean
Abstract
Kermack과 Mckendrick(1927)이 제안한 SIR 모형은 감염병의 확산과정을 설명하기 위한 가장 대표적인 방법이다. 코로나19와 MERS 같은 호흡기 질환은 사람과 사람의 접촉에 의해 전파되는 감염병으로 사람과 사람의 연결을 모형화하는 네트워크 모형을 이용하여 감염병 모형을 구축할 수 있다. 네트워크 모형에서 개개인은 각 노드(node, 꼭짓점)로 표시되며, 노드 간의 연결을 엣지(edge, 변)라 표시한다. 이때의 노드는 SIR 모형에서의 S(감염대상군), I(감염군), R(회복군) 중 하나의 상태를 나타낸다. 감염대상군(S)의 한 사람이 감염군(I)의 사람들 중 한 사람과 접촉했을 때, 그 사람은 감염되어 감염대상군에서 감염군으로 이동하게 되고, 그 즉시 다른 사람을 감염시킬 수 있게 된다. 서로 다른 노드가 엣지로 연결되어 있을 때, 각각의 상태가 S와 I라면, 이 연결을 통해 감염이 전파된다고 볼 수 있다. 즉, 엣지는 개체 간의 접촉 또는 전파 가능성을 나타내고, 네트워크 구조는 물리적 상호작용 또는 사회적 연결성을 반영하며, 사회 연결망 모형에서 개인과 개인 사이의 연결을 질병 확산 모형에서는 감염병의 전파로 나타낸다. 본 연구에서는 감염병의 확산과정을 설명하기 위하여 네트워크에 기반한 모형 구축 방법으로 두 가지 방법을 이용하였다. 먼저 확률적 네트워크 모형인 EBCM (Edge-Based Compartment Model)을 이용하여 감염병 모형을 구축하고, 모형 추정을 위하여 Dynamic Survival Analysis(DSA) 방법을 적용하였다. 두 번째로는 Random graph로 출발하여 네트워크에 기반을 두고 확률 모형을 구축하여 감염병 모형의 모수를 추정하는 방법을 이용하였다. 두 번째 방법은 상대적으로 네트워크가 작거나, 질병의 확산과정을 초기 시점에 적용하는 모형이다. 본 연구에서 이용된 두 방법을 2020년 서울시의 코로나19 확진자 데이터에 적합시켜 모형의 적합도를 실제 데이터와 비교하여 검증하였다.
The SIR model, proposed by Kermack and McKendrick in 1927, is the mostrepresentative method for describing the spread of infectious diseases. Respiratorydiseases such as COVID-19 and MERS are infectious diseases that spread throughhuman-to-human contact, and infectious disease models can be built using networkmodels that simulate human-to-human connections. In a network model, eachindividual is represented by a node(vertex), and the connections between nodes arerepresented by edges. A node can be in one of the following states in the SIR model: (Susceptible), (Infected), or (Recovered/Removed). When a person in thesusceptible( ) comes into contact with an individual in the infected( ), the personbecomes infected, moves from the susceptible group to the infected group, andimmediately gains the ability to infect other people. When different nodes areconnected by edges, if their respective states are and , then we can say that theinfection is transmitted through this connection. In other words, edges represent thecontact or transmission potential between individuals, the network structure reflectsphysical interaction or social connectivity, and the connections between individuals inthe social network model are represented by the transmission of infectious diseases inthe epidemic model. In this study, two network-based modeling methods were used todescribe the spread of infectious diseases. First, the Edge-Based CompartmentModel(EBCM), a probabilistic network model, was used to build an infectious diseasemodel, and the Dynamic Survival Analysis(DSA) method was applied to estimate themodel. The second method involves starting with a random graph and building aprobabilistic model based on the network to estimate the parameters of the infectiousdisease model. This second method is suitable for a relatively small network or anearly stage of the disease spread process. Both methods used in this study wereapplied to the data of COVID-19 cases in Seoul in 2020 to verify the suitability ofthe model by comparing it with the actual data.
The SIR model, proposed by Kermack and McKendrick in 1927, is the mostrepresentative method for describing the spread of infectious diseases. Respiratorydiseases such as COVID-19 and MERS are infectious diseases that spread throughhuman-to-human contact, and infectious disease models can be built using networkmodels that simulate human-to-human connections. In a network model, eachindividual is represented by a node(vertex), and the connections between nodes arerepresented by edges. A node can be in one of the following states in the SIR model: (Susceptible), (Infected), or (Recovered/Removed). When a person in thesusceptible( ) comes into contact with an individual in the infected( ), the personbecomes infected, moves from the susceptible group to the infected group, andimmediately gains the ability to infect other people. When different nodes areconnected by edges, if their respective states are and , then we can say that theinfection is transmitted through this connection. In other words, edges represent thecontact or transmission potential between individuals, the network structure reflectsphysical interaction or social connectivity, and the connections between individuals inthe social network model are represented by the transmission of infectious diseases inthe epidemic model. In this study, two network-based modeling methods were used todescribe the spread of infectious diseases. First, the Edge-Based CompartmentModel(EBCM), a probabilistic network model, was used to build an infectious diseasemodel, and the Dynamic Survival Analysis(DSA) method was applied to estimate themodel. The second method involves starting with a random graph and building aprobabilistic model based on the network to estimate the parameters of the infectiousdisease model. This second method is suitable for a relatively small network or anearly stage of the disease spread process. Both methods used in this study wereapplied to the data of COVID-19 cases in Seoul in 2020 to verify the suitability ofthe model by comparing it with the actual data.