• Journal of Information Technology Applications and Management
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• v.31 no.1
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• pp.1-9
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• 2024

Predicting the spread of COVID-19 remains a challenge due to the complexity of the disease and its evolving nature. This study presents an integrated approach using the classic SIR model for infectious diseases, enhanced by the chemical master equation (CME). We employ a Monte Carlo method (SSA) to solve the model, revealing unique aspects of the SARS-CoV-2 virus transmission. The study, a first of its kind in Korea, adopts a step-by-step and complementary approach to model prediction. It starts by analyzing the epidemic's trajectory at local government levels using both basic and stochastic SIR models. These models capture the impact of public health policies on the epidemic's dynamics. Further, the study extends its scope from a single-infected individual model to a more comprehensive model that accounts for multiple infections using the jump SIR prediction model. The practical application of this approach involves applying these layered and complementary SIR models to forecast the course of the COVID-19 epidemic in small to medium-sized local governments, particularly in Gangnam-gu, Seoul. The results from these models are then compared and analyzed.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1089-1099
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• 2010

An SIR epidemic model with pulse vaccination and time delay describing infection period is investigated. The global attractiveness of the infection-free periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Our results indicate that a large vaccination rate or a short period of pulsing leads to the eradication of the disease.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.919-928
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• 2018

In this paper, we consider the admissible control problem for the linear systems by using the solution of the Hausdorff moment problem. In addition, we consider the admissible control problem for SIR epidemic model.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.45-67
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• 2021

In this paper, a mathematical dynamical system involving both deterministic (with or without delay) and stochastic "SIR" epidemic model with nonlinear incidence rate in a continuous reactor is considered. A profound qualitative analysis is given. It is proved that, for both deterministic models, if ��d > 1, then the endemic equilibrium is globally asymptotically stable. However, if ��d ≤ 1, then the disease-free equilibrium is globally asymptotically stable. Concerning the stochastic model, the Feller's test combined with the canonical probability method were used in order to conclude on the long-time dynamics of the stochastic model. The results improve and extend the results obtained for the deterministic model in its both forms. It is proved that if ��s > 1, the disease is stochastically permanent with full probability. However, if ��s ≤ 1, then the disease dies out with full probability. Finally, some numerical tests are done in order to validate the obtained results.

• Environmental and Resource Economics Review
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• v.30 no.1
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• pp.27-48
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• 2021

We extend and modify the canonical epidemiology model of Eichenbaum, Rebelo and Trabandt (2020) to investigate the general equilibrium effects of COVID-19 spread in the Korean economy when vaccine, treatment and social distancing are available. Particularly, we develop a SIR-macro model which considers possibility of moral inattention of the overconfident agents through which people is more likely to be infected. Our model implies that people's decision to cut back on consumption and work reduces the severity of the epidemic and thus exacerbate the size of the economic recession caused by the epidemic. Another finding is that the average 13 weeks to develop the vaccine and treatment will lead to 2% drop of consumption.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.301-312
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• 2015

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.

• The Journal of Society for e-Business Studies
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• v.19 no.4
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• pp.31-43
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• 2014

These days a lot of cyber attacks are exploiting the vulnerabilities of S/W. According to the trend of vulnerabilities is announced periodically, security directions are suggested and security controls are updated with this trend. Nevertheless, cyber attacks like hacking during the year 2011 are increased by 81% compared to 2010. About 75% of these cyber attacks are exploiting the vulnerabilities of S/W itself. In this paper, we have suggested a VIR model, which is a spread model of malware infection for measuring economic loss by S/W vulnerability, by applying the SIR model which is a epidemic model. It is applied to estimate economic loss by HWP(Hangul word) S/W vulnerabilities.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.271-280
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• 2014

Foot-and-mouth Disease (FMD) is a highly infectious and fatal viral livestock disease that affects cloven-hoofed animals domestic and wild and the FMD outbreak in Korea in 2010/2011 was a disastrous incident for the country and the economy. Thus, efforts at the national level are put to prevent foot-and-mouth disease and to reduce the damage in the case of outbreak. As one of these efforts, it is useful to study the spread of the disease by using probabilistic model. In fact, after the FMD epidemic in the UK occurred in 2001, many studies have been carried on the spread of the disease using a variety of stochastic models as an effort to prepare future outbreak of FMD. However, for the FMD outbreak in Korea occurred in 2010/2011, there are few study by utilizing probabilistic model. This paper assumes a stochastic spatial-temporal susceptible-infectious-removed (SIR) epidemic model for the 2010/2011 FMD outbreak to understand spread of the disease. Since data on infections of FMD disease during 2010/2011 outbreak of Aniaml and Plant Quarantine Agency and on the livestock farms from the nationwide census in 2011 of Statistics Korea do not have detail informations on address or missing values, we generate detail information on address by randomly allocating farms within corresponding Si/Gun area. The kernel function is estimated using the infection data and by using simulations, the susceptibility and transmission of the spatial-temporal stochastic SIR models are determined.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.297-307
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• 2017

The epidemic model is used to model the spread of disease and to control the disease. In this research, we utilize SEIR model which is one of applications the SIR model that incorporates Exposed step to the model. The SEIR model assumes that a people in the susceptible contacted infected moves to the exposed period. After staying in the period, the infectee tends to sequentially proceed to the status of infected, recovered, and removed. This type of infection can be used for research in cases where there is a latency period after infectious disease. In this research, we collected respiratory infectious disease data for the Middle East Respiratory Syndrome Coronavirus (MERSCoV). Assuming that the spread of disease follows a stochastic process rather than a deterministic one, we utilized the Poisson process for the variation of infection and applied epidemic model to the stochastic chemical reaction model. Using observed pandemic data, we estimated three parameters in the SIER model; exposed rate, transmission rate, and recovery rate. After estimating the model, we applied the fitted model to the explanation of spread disease. Additionally, we include a process for generating the Exposed trajectory during the model estimation process due to the lack of the information of exact trajectory of Exposed.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.57-66
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• 2017

SIR model (Kermack and McKendrik, 1927) is one of the most popular method to explain the spread of disease, In order to construct SIR model, we need to estimate transition rate parameter and recovery rate parameter. If we don't have any information of the two rate parameters, we should estimate using observed whole trajectory of pandemic of disease. Thus, with restricted observed data, we can't estimate rate parameters. In this research, we introduced Reed-Frost model (Andersson and Britton, 2000) to calculate the probability of infection in the early stage of pandemic with the restriction of data. When we have an initial number of susceptible and infected, and a final number of infected, we can apply Reed - Frost model and we can get the probability of infection. We applied the Reed - Frost model to the Vibrio cholerae pandemic data from Republic of the Cameroon and calculated the probability of infection at the early stage. We also construct SIR model using the result of Reed - Frost model.