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Original Article
Inherently high uncertainty in predicting the time evolution of epidemics
Seung-Nam Park, Hyong-Ha Kim, Kyoung Beom Lee
Epidemiol Health. 2021;43:e2021014.   Published online February 8, 2021
DOI: https://doi.org/10.4178/epih.e2021014
  • 13,154 View
  • 310 Download
  • 3 Web of Science
  • 2 Crossref
AbstractAbstract AbstractSummary PDF
Abstract
OBJECTIVES
Amid the spread of coronavirus disease 2019 (COVID-19), with its high infectivity, we have relied on mathematical models to predict the temporal evolution of the disease. This paper aims to show that, due to active behavioral changes of individuals and the inherent nature of infectious diseases, it is complicated and challenging to predict the temporal evolution of epidemics.
METHODS
A modified susceptible-exposed-infectious-hospitalized-removed (SEIHR) compartment model with a discrete feedback-controlled transmission rate was proposed to incorporate individuals’ behavioral changes into the model. To figure out relative uncertainties in the infection peak time and the fraction of the infected population at the peak, a deterministic method and 2 stochastic methods were applied.
RESULTS
A relatively small behavioral change of individuals with a feedback constant of 0.02 in the modified SEIHR model resulted in a peak time delay of up to 50% using the deterministic method. Incorporating stochastic methods into the modified model with a feedback constant of 0.04 suggested that the relative random uncertainty of the maximum fraction of infections and that of the peak time for a population of 1 million reached 29% and 9%, respectively. Even without feedback, the relative uncertainty of the peak time increased by up to 20% for a population of 100,000.
CONCLUSIONS
It is shown that uncertainty originates from stochastic properties of infections. Without a proper selection of the evolution scenario, active behavioral changes of individuals could serve as an additional source of uncertainty.
Summary
Korean summary
이 논문은 감염병에 대응하는 개인의 능동적 행동 변화와 감염병의 고유한 특성 때문에 그 진행을 예측하는 것은 복잡하고 도전적인 작업이라는 것을 보이기 위한 것이다. 이런 행동 변화를 고려하기 위하여 감염률에 피드백 제어를 줄 수 있는 SEIHR 수정 모델을 제안하였다. 최대 감염까지 경과 시간과 최대 감염률의 상대 불확도를 계산하기 위하여 하나의 결정론적 방법과 두 가지의 확률론적 방법 적용하였다. 감염병 예측의 불확도는 감염의 확률론적 성질에 기인하는 것을 알 수 있었다. 적절한 진행의 시나리오를 설정하지 못할 경우 개인의 능동적 행동 변화가 추가적인 불확도 요인이 될 것이다.
Key Message
This paper is to show that, due to active behavioral changes of individuals and inherent natures of infectious diseases, it is complicated and challenging to predict the temporal evolutions. A modified-SEIHR compartment model with a discretely feedback-controlled transmission rate was proposed to incorporate the behavioral changes of individuals into the model. To figure out relative uncertainties in the infection peak times and the fraction of the infected population at the peak, a deterministic method and two stochastic methods were applied. It is shown that the uncertainty of the prediction originates from stochastic properties of the infections. Without a proper selection of the evolution scenarios, the active behavioral changes of individuals could cause an additional uncertainty.

Citations

Citations to this article as recorded by  
  • Modeling Supply and Demand Dynamics of Vaccines against Epidemic-Prone Pathogens: Case Study of Ebola Virus Disease
    Donovan Guttieres, Charlot Diepvens, Catherine Decouttere, Nico Vandaele
    Vaccines.2023; 12(1): 24.     CrossRef
  • Evolution and consequences of individual responses during the COVID-19 outbreak
    Wasim Abbas, Masud M. A., Anna Park, Sajida Parveen, Sangil Kim, Siew Ann Cheong
    PLOS ONE.2022; 17(9): e0273964.     CrossRef
COVID-19: Brief Communication
Analyzing the effects of social distancing on the COVID-19 pandemic in Korea using mathematical modeling
Sunhwa Choi, Moran Ki
Epidemiol Health. 2020;42:e2020064.   Published online September 7, 2020
DOI: https://doi.org/10.4178/epih.e2020064
  • 15,440 View
  • 526 Download
  • 16 Web of Science
  • 15 Crossref
AbstractAbstract AbstractSummary PDFSupplementary Material
Abstract
OBJECTIVES
During the 6 months since the first coronavirus disease 2019 (COVID-19) patient was diagnosed in Korea on January 20, 2020, various prevention and control measures have been implemented according to the COVID-19 epidemic pattern. Therefore, this study aimed to estimate the reproductive numbers (R) for each epidemic stage to analyze the effects of the preventive measures and to predict the COVID-19 transmission trends.
METHODS
We estimated the transmission rates for each epidemic stage by fitting a COVID-19 transmission model, based on a deterministic mathematical model, to the data on confirmed cases. The effects of preventive measures such as social distancing by time period were analyzed, and the size and trends of future COVID-19 outbreaks were estimated.
RESULTS
The value of R was 3.53 from February18, 2020 to February 28, 2020, and the mean R reduced to 0.45 from March 14, 2020 to April 29, 2020, but it significantly increased to 2.69 from April 30, 2020 to May13, 2020 and it was maintained at 1.03 from May 14, 2020 to July 23, 2020.
CONCLUSIONS
According to the estimated R, it had fallen to below 1 and was maintained at that level owing to the isolation of infected persons by the public health authorities and social distancing measures followed by the general public. Then, the estimated R increased rapidly as the contact among individuals increased during the long holiday period from April 30, 2020 to May 5, 2020. Thereafter, the value of R dropped, with the continued use of preventive measures but remained higher than 1.00, indicating that the COVID-19 outbreak can be prolonged and develop into a severe outbreak at any time.
Summary
Korean summary
수학적 모델링을 통하여 코로나-19 유행양상에 따른 시기별 감염재생산수(reproductive number)를 추정하고, 시기별 방역정책의 효과를 분석하여 향후 유행의 규모와 유행 종료 시점 등을 예측하였다. 그 결과, 4월30일부터 5월5일까지의 긴 연휴 기간을 통해 사람들 간의 접촉이 증가하면서 감염재생산수가 급격히 증가하였고(4월 30일 - 5월 13일까지 평균 R=2.69), 그 후, 지속적인 방역조치로 인해 5월 14일-7월 23일까지 평균 R=1.03로 감소하였으나, 여전히 1보다 큰 값으로 나타나, 코로나-19유행이 지속되고 있으며 언제라도 다시 큰 유행으로 커질 수 있다고 예측되었다.

Citations

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  • Analysis of Symptoms and Demographic Characteristics in Diagnosis of COVID-19 by Logistic Regression Model
    Caner Tanış
    Selçuk Üniversitesi Fen Fakültesi Fen Dergisi.2024; 50(1): 1.     CrossRef
  • Mathematical Modeling of COVID-19 Transmission and Intervention in South Korea: A Review of Literature
    Hyojung Lee, Sol Kim, Minyoung Jeong, Eunseo Choi, Hyeonjeong Ahn, Jeehyun Lee
    Yonsei Medical Journal.2023; 64(1): 1.     CrossRef
  • 코로나19 핵심 지표 산출체계 국제 비교 및 활용도 제고 방안 연구
    나애 이, 연경 김, 승필 정, 우주 이, 주환 오, 승식 황
    Public Health Weekly Report.2023; 16(29): 973.     CrossRef
  • The Effect of COVID–19 on Pediatric Intussusception: A Retrospective Study of a Single Center in South Korea with 10–Year Experience
    Yeo Jin Yoo, Bo-Kyung Je, Ga Young Choi, Jee Hyun Lee, Sunkyu Choi, Ji Young Lee
    Journal of the Korean Society of Radiology.2022; 83(2): 304.     CrossRef
  • Trends of Internet Search Volumes for Major Depressive Disorder Symptoms During the COVID-19 Pandemic in Korea: An Interrupted Time-Series Analysis
    Jieun Kim, Juhui Han, Byung Chul Chun
    Journal of Korean Medical Science.2022;[Epub]     CrossRef
  • A Novel Approach on Deep Learning—Based Decision Support System Applying Multiple Output LSTM-Autoencoder: Focusing on Identifying Variations by PHSMs’ Effect over COVID-19 Pandemic
    Yong-Ju Jang, Min-Seung Kim, Chan-Ho Lee, Ji-Hye Choi, Jeong-Hee Lee, Sun-Hong Lee, Tae-Eung Sung
    International Journal of Environmental Research and Public Health.2022; 19(11): 6763.     CrossRef
  • Changes in the pattern and disease burden of acute viral respiratory infections before and during the COVID-19 pandemic
    Chungmin Park, Donghan Lee, Inho Kim, Sujin Park, Gyehee Lee, Sangwoo Tak
    Osong Public Health and Research Perspectives.2022; 13(3): 203.     CrossRef
  • Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data
    Hardik Joshi, Brajesh Kumar Jha, Mehmet Yavuz
    Mathematical Biosciences and Engineering.2022; 20(1): 213.     CrossRef
  • Exploring spatial distribution of social vulnerability and its relationship with the Coronavirus disease 2019: the Capital region of South Korea
    Donghyun Kim
    BMC Public Health.2022;[Epub]     CrossRef
  • Impact of Nonpharmaceutical Interventions on the Incidence of Respiratory Infections During the Coronavirus Disease 2019 (COVID-19) Outbreak in Korea: A Nationwide Surveillance Study
    Kyungmin Huh, Jaehun Jung, Jinwook Hong, MinYoung Kim, Jong Gyun Ahn, Jong-Hun Kim, Ji-Man Kang
    Clinical Infectious Diseases.2021; 72(7): e184.     CrossRef
  • Statistical Analysis of Patients Visiting Department of Acupuncture and Moxibustion in Korean Medicine Hospital Before and After COVID-19 - Focusing on a Korean Medicine Hospital in Daejeon -
    Young Rok Lee, Hyun Ji Cha, Hyeon Kyu Choi, Min Ju Kim, Beom Seok Kim, Ki Jung Sung, Ju Hyun Jeon, Eun Seok Kim, Young Il Kim
    Journal of Korean Medicine.2021; 42(2): 31.     CrossRef
  • Dissection of non-pharmaceutical interventions implemented by Iran, South Korea, and Turkey in the fight against COVID-19 pandemic
    Mohammad Keykhaei, Sogol Koolaji, Esmaeil Mohammadi, Reyhaneh Kalantar, Sahar Saeedi Moghaddam, Arya Aminorroaya, Shaghayegh Zokaei, Sina Azadnajafabad, Negar Rezaei, Erfan Ghasemi, Nazila Rezaei, Rosa Haghshenas, Yosef Farzi, Sina Rashedi, Bagher Larijan
    Journal of Diabetes & Metabolic Disorders.2021; 20(2): 1919.     CrossRef
  • Hybrid Model-Based Simulation Analysis on the Effects of Social Distancing Policy of the COVID-19 Epidemic
    Bong Gu Kang, Hee-Mun Park, Mi Jang, Kyung-Min Seo
    International Journal of Environmental Research and Public Health.2021; 18(21): 11264.     CrossRef
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    Daniil Pilchen, Rebekah Wilson
    Organised Sound.2021; 26(3): 340.     CrossRef
  • Comparative Analysis of Patients Visiting Department of Korean Internal Medicine in a Korean Medicine Hospital Before and During COVID-19 - From July 2018 to June 2021 at Wonkwang University Jeonju Korean Medicine Hospital -
    Ji-eun Lee, Yong-jeen Shin, Sun-ho Shin
    The Journal of Internal Korean Medicine.2021; 42(6): 1255.     CrossRef
COVID-19: Methods
Individual-based simulation model for COVID-19 transmission in Daegu, Korea
Woo-Sik Son, RISEWIDs Team
Epidemiol Health. 2020;42:e2020042.   Published online June 15, 2020
DOI: https://doi.org/10.4178/epih.e2020042
  • 14,029 View
  • 294 Download
  • 7 Web of Science
  • 5 Crossref
AbstractAbstract AbstractSummary PDFSupplementary Material
Abstract
OBJECTIVES
The aims of this study were to obtain insights into the current coronavirus disease 2019 (COVID-19) epidemic in the city of Daegu, which accounted for 6,482 of the 9,241 confirmed cases in Korea as of March 26, 2020, to predict the future spread, and to analyze the impact of school opening.
METHODS
Using an individual-based model, we simulated the spread of COVID-19 in Daegu. An individual can be infected through close contact with infected people in a household, at work/school, and at religious and social gatherings. We created a synthetic population from census sample data. Then, 9,000 people were randomly selected from the entire population of Daegu and set as members of the Shincheonji Church. We did not take into account population movements to and from other regions in Korea.
RESULTS
Using the individual-based model, the cumulative confirmed cases in Daegu through March 26, 2020, were reproduced, and it was confirmed that the hotspot, i.e., the Shincheonji Church had a different probability of infection than non-hotspot, i.e., the Daegu community. For 3 scenarios (I: school closing, II: school opening after April 6, III: school opening after April 6 and the mean period from symptom onset to hospitalization increasing to 4.3 days), we predicted future changes in the pattern of COVID-19 spread in Daegu.
CONCLUSIONS
Compared to scenario I, it was found that in scenario III, the cumulative number of patients would increase by 107 and the date of occurrence of the last patient would be delayed by 92 days.
Summary
Korean summary
신천지 교인 집단이 hotspot이 되어 지역사회로 전파된 대구의 COVID-19 확산을 시뮬레이션하였다. Individual based model을 이용하여 신천지 교인 집단, 즉 hotspot과 non-hotspot이 서로 다른 감염 확률을 갖고 있음을 확인하였으며, 4월 6일로 예정된 개학이 대구 지역 COVID-19 확산에 어떤 영향을 미칠지 분석하였다.

Citations

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  • Using simulation modelling and systems science to help contain COVID‐19: A systematic review
    Weiwei Zhang, Shiyong Liu, Nathaniel Osgood, Hongli Zhu, Ying Qian, Peng Jia
    Systems Research and Behavioral Science.2023; 40(1): 207.     CrossRef
  • Mathematical Modeling of COVID-19 Transmission and Intervention in South Korea: A Review of Literature
    Hyojung Lee, Sol Kim, Minyoung Jeong, Eunseo Choi, Hyeonjeong Ahn, Jeehyun Lee
    Yonsei Medical Journal.2023; 64(1): 1.     CrossRef
  • Transition from growth to decay of an epidemic due to lockdown
    Hamid Khataee, Jack Kibble, Istvan Scheuring, Andras Czirok, Zoltan Neufeld
    Biophysical Journal.2021; 120(14): 2872.     CrossRef
  • A Full-Scale Agent-Based Model to Hypothetically Explore the Impact of Lockdown, Social Distancing, and Vaccination During the COVID-19 Pandemic in Lombardy, Italy: Model Development
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    JMIRx Med.2021; 2(3): e24630.     CrossRef
  • Comparison of Psychosocial Distress in Areas With Different COVID-19 Prevalence in Korea
    Mina Kim, In-Hoo Park, Young-Shin Kang, Honey Kim, Min Jhon, Ju-Wan Kim, Seunghyong Ryu, Ju-Yeon Lee, Jae-Min Kim, Jonghun Lee, Sung-Wan Kim
    Frontiers in Psychiatry.2020;[Epub]     CrossRef
COVID-19: Original Article
Prediction of COVID-19 transmission dynamics using a mathematical model considering behavior changes in Korea
Soyoung Kim, Yu Bin Seo, Eunok Jung
Epidemiol Health. 2020;42:e2020026.   Published online April 13, 2020
DOI: https://doi.org/10.4178/epih.e2020026
  • 23,484 View
  • 1,327 Download
  • 51 Web of Science
  • 50 Crossref
AbstractAbstract AbstractSummary PDFSupplementary Material
Abstract
OBJECTIVES
Since the report of the first confirmed case in Daegu on February 18, 2020, local transmission of coronavirus disease 2019 (COVID-19) in Korea has continued. In this study, we aimed to identify the pattern of local transmission of COVID-19 using mathematical modeling and predict the epidemic size and the timing of the end of the spread.
METHODS
We modeled the COVID-19 outbreak in Korea by applying a mathematical model of transmission that factors in behavioral changes. We used the Korea Centers for Disease Control and Prevention data of daily confirmed cases in the country to estimate the nationwide and Daegu/Gyeongbuk area-specific transmission rates as well as behavioral change parameters using a least-squares method.
RESULTS
The number of transmissions per infected patient was estimated to be about 10 times higher in the Daegu/Gyeongbuk area than the average of nationwide. Using these estimated parameters, our models predicts that about 13,800 cases will occur nationwide and 11,400 cases in the Daegu/Gyeongbuk area until mid-June.
CONCLUSIONS
We mathematically demonstrate that the relatively high per-capita rate of transmission and the low rate of changes in behavior have caused a large-scale transmission of COVID-19 in the Daegu/Gyeongbuk area in Korea. Since the outbreak is expected to continue until May, non-pharmaceutical interventions that can be sustained over the long term are required.
Summary
Korean summary
본 논문은 행동변화를 고려한 수학적 모델을 이용하여 코로나바이러스병-19의 유행 양상을 분석하고 총 환자수와 유행기간을 예측하고자 한다. 질병관리본부 확진자 데이터를 이용하여 전국과 대구·경북 지역의 감염전파율과 행동변화율을 추정하였다. 3월 10일까지의 데이터를 기준으로 전국적으로 6월 중순까지 약 13,000명, 대구·경북지역의 경우 5월 말까지 약 11,000명의 환자가 발생할 것으로 예측된다.

Citations

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COVID-19: Original Article
Estimating the reproductive number and the outbreak size of COVID-19 in Korea
Sunhwa Choi, Moran Ki
Epidemiol Health. 2020;42:e2020011.   Published online March 12, 2020
DOI: https://doi.org/10.4178/epih.e2020011
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AbstractAbstract AbstractSummary PDFSupplementary Material
Abstract
OBJECTIVES
Since the first novel coronavirus disease 2019 (COVID-19) patient in Korea was diagnosed on January 20, 2020, 30 patients were diagnosed until February 17, 2020. However, 5,298 additional patients were confirmed until March 4, 2020. Therefore, our objective was to estimate the reproduction number (<i>R</i>) and evaluate the effectiveness of preventive measures.
METHODS
A COVID-19 transmission model (SEIHR) was established to suit the Korean outbreak. The number of daily confirmed cases in Daegu and North Gyeongsang Province (NGP), the main area of outbreak, was used. The first patient’ symptom onset date in the Daegu/NGP outbreak was assumed as January 22, 2020. The <i>R</i> according to the start date of the effect of preventive measures was estimated.
RESULTS
The estimated <i>R</i> in Hubei Province, China, was 4.0281, whereas the estimated initial <i>R</i> in Korea was 0.555, but later in Daegu/NGP, the value was between 3.472 and 3.543. When the transmission period decreases from 4-day to 2-day, the outbreak ends early, but the peak of the epidemic increases, and the total number of patients does not change greatly. It was found that, if transmission rate decreases, the outbreak ends early, and the size of the peak and the total number of patients also decreases.
CONCLUSIONS
To end the COVID-19 epidemic, efforts to reduce the spread of the virus, such as social distancing and wearing masks, are absolutely crucial with the participation of the public, along with the policy of reducing the transmission period by finding and isolating patients as quickly as possible through the efforts of the quarantine authorities.
Summary
Korean summary
수학적 모델링을 통하여 코로나-19 감염재생산수( R )와 대구, 경북의 유행 규모와 유행 종료 시점 등을 예측해보았다. 그 결과 중국 후베이성의 R=4, 한국 초기 30일간의 유행은 R=0.5, 대구/경북의 3월 4일까지의 유행은 R=3.5 수준으로 나타났다. 하지만 방역당국의 적극적인 코로나-19검사로 환자들의 감염전파기간이 짧아지고, 국민들의 마스크 쓰기, 사회적 거리두기 등의 감염 예방조치 적극 참여로 전파율이 낮아져 5월 1일경에 하루 환자 1명 수준으로 예측되었다.

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