Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
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확률적 방법에 기반한 질병 확산 모형의 구축

Development of epidemic model using the stochastic method

  • 류수락 (대구대학교 대학원 통계학과) ;
  • 최보승 (대구대학교 전산통계학과)
  • Ryu, Soorack (Department of Statistics, Daegu University) ;
  • Choi, Boseung (Department of Statistics and Computer Science, Daegu University)
  • 투고 : 2015.01.05
  • 심사 : 2015.02.10
  • 발행 : 2015.03.31
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초록

본 연구는 전염병의 확산 과정을 설명하기 위한 질병 확산 모형을 구축 하고자 하였다. 질병의 확산 과정은 결정적인 과정과 확률적인 과정으로 크게 분류할 수 있다. 대부분의 연구가 질병의 확산 과정을 결정적 과정으로 움직인다고 가정을 하고 상미분방정식을 이용하여 모형을 구축하였다. 본 연구에서는 질병 확산 모형인 SIR (Suspectible - Infectious - Recovered) 모형을 기반으로 하여 질병의 확산 예측 모형을 구현하고자 하였다. 최소제곱법을 이용하여 모수를 추정한 후, 상미분방정식을 이용한 결정적 모형 방법과 더불어 Gillespie가 제안한 방법에 기반하여 확률적인 과정을 따르는 모형 적합을 함께 시도하였다. 본 연구에서 소개된 방법들은 질병관리본부의 2001년 1월부터 2002년 3월까지의 국내 말라리아 주별 발병자 수 자료를 이용하여 모형 적합을 시도 하였으며, 그 결과 구현된 모형이 실제 질병의 확산과정을 잘 설명하였다.

The purpose of this paper is to establish the epidemic model to explain the process of disease spread. The process of disease spread can be classified into two types: deterministic process and stochastic process. Most studies supposed that the process follows the deterministic process and established the model using the ordinary differential equation. In this article, we try to build the disease spread prediction model based on the SIR (Suspectible - Infectious - Recovered) model. we first estimated the model parameters using least squared method and applied to a deterministic model using ordinary differential equation. we also applied to a stochastic model based on Gillespie algorithm. The methods introduced in this paper are applied to the data on the number of cases of malaria every week from January 2001 to March 2003, released by Korea Centers for Disease Control and Prevention. As a result, we conclude that our model explains well the process of disease spread.

키워드

참고문헌

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피인용 문헌

  1. An estimation method for stochastic reaction model vol.26, pp.4, 2015, https://doi.org/10.7465/jkdi.2015.26.4.813
  2. 베이지안 음이항 분기과정을 이용한 한국 메르스 발생 연구 vol.28, pp.1, 2015, https://doi.org/10.7465/jkdi.2017.28.1.153
  3. Reed - Frost 모형을 이용한 전염병 감염 확률 추정 vol.28, pp.1, 2015, https://doi.org/10.7465/jkdi.2017.28.1.57
  4. SEIR 모형을 이용한 전염병 모형 예측 연구 vol.28, pp.2, 2015, https://doi.org/10.7465/jkdi.2017.28.2.297