• 대한수학회논문집
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• 제18권1호
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• pp.133-149
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• 2003

Local stability of steady states of an epidemic model is considered. An age structured S-I-R epidemic model with separable inter-cohort force of infection with external force is considered. Stability result for the nontrivial steady states is obtained.

• 대한산업공학회지
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• 제40권2호
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• pp.163-171
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• 2014

Epidemic models are used to analyze the spreading of epidemic diseases, estimate public health needs, and assess the effectiveness of mitigation strategies. Modeling scope of an epidemic model ranges from the regional scale to national and global scale. Most of the epidemic models developed in Korea are at the national scale using the equation-based model. While these models are useful for designing and evaluating national public health policies, they do not provide sufficient details. As an alternative, individual-based models at the regional scale are often used to describe disease spreading, so that various mitigation strategies can be designed and tested. This paper presents an individual-based epidemic spreading model at regional scale. This model incorporates 2005 census data to build the synthetic population in the model representing Daejeon in 2005. The model's capability is demonstrated by an example where we assess the effectiveness of several mitigation strategies using the model.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.

• 대한전기학회논문지
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• 제33권11호
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• pp.440-446
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• 1984

This thesis investigates the quantitative aspect of epidemic phenomena utilizing the analytical method of discrete time systems based on the theory of Markov processes. In particular, the pattern on the epidemic character of Influenza was analyzed by the mathematical model of Influenza system, which is derived according to the ecologic relationship between five epidemiolgic states of individuals. The quantitative aspects of the model was characterized by digital computer simulations. The main results were obtained as follows: 1) A Markovian model of influenza system represents accurate spead curve. 2) The latent period of influenza has the standard deviation of 1.98 and also the incubation period is 2.68. 3) If the value of susceptibilities in the pre-epidemic period is less than 20% of the population, the epidemic will occur sporadically. 4) The initial value of susceptibilties obtained by this markov theory is less about 10% of total population than the obtained value according to the deterministic model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권1호
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• pp.55-65
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• 2013

The purpose of this paper is to prove existence of solutions of an SIRS epidemic model with time delay of continuous type and the variable incidence rate and to investigate some asymptotic behaviors of the SIRS epidemic model. An example illustrating the stability of the model is given. The results extend the corresponding results in the literature.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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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.

• Journal of the Korean Statistical Society
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• 제22권1호
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• pp.133-138
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• 1993

We consider two estimators of the infection rate in the simple stochastic epidemic model. It is shown that the maximum likelihood estimator of teh infection rate under the discrete time observation does not have the moment of any positive order. Some properties of the Choi-Severo estimator, an approximation to the maximum likelihood estimator, are also investigated.

• 대한수학회논문집
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• 제26권2호
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• pp.321-338
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• 2011

In this paper, a class of delayed epidemic model with diffusion is investigated. By analyzing the associated characteristic transcendental equation, its linear stability is investigated and Hopf bifurcation is demonstrated. Some explicit formulae determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulation are also carried out to support our analytical findings. Finally, biological explanations and main conclusions are given.

• 디지털융복합연구
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• 제16권7호
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• pp.259-265
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• 2018

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.

• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.247-253
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• 1998

영과잉-포아송모형에서 변화시점이 있는 경우, 돌출대립가설에 대한 우도비검정을 이용하여 변화시점의 유 무를 알아보았다. 변화시점에 대한 추정은 최소제곱법을 이용하였고 이를 최우추정법을 이용하기 위한 초기치로 활용하였다. 또한 대립가설에 대한 몇가지 흥미있는 모수들을 적률법을 이용하여 추정하였다. 모의실험을 통하여 이들 추정 량을 비교하였고 결과 변화시점에 대한 추정은 최소제곱법보다는 최우추정법이 바람직하게 나타났고 흥미있는 몇가지 모수들에 대해서는 최우추정량이 적률추정량보다 우수하게 나타났다.