• Korean Journal of Mathematics
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• v.13 no.2
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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.

• Journal of Biomedical Engineering Research
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• v.12 no.3
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• pp.171-176
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• 1991

A solution for the course of the general deterministic epidemic model is obtained by elementary series expansion. This is valid over all times, and appears to hold accurate]y over a very wide range of population and threshould parameter values. This algorithm can be more efficient than either numerical or recursive procedures in terms of the number of operations required to evaluate a sequence of points along the course of the epidemic.

• 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.

• Journal of the Korean Statistical Society
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• v.22 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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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.

• Journal of Preventive Medicine and Public Health
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• v.51 no.6
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• pp.326-328
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• 2018

As over 1000 new cases of HIV/AIDS occur in Korea annually, preventive health programs against HIV/AIDS are urgently needed. Since phylodynamic studies have been suggested as a way to understand how infectious diseases are transmitted and evolve, phylodynamic inferences can be a useful tool for HIV/AIDS research. In particular, phylodynamic models are helpful for dating the origins of an epidemic and estimating its basic reproduction number. Thus, the introduction of phylodynamics would be a highly valuable step towards controlling the HIV/AIDS epidemic in Korea.

• Korean Journal of Veterinary Research
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• v.38 no.4
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• pp.818-822
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• 1998

The persistence of porcine epidemic diarrhea virus(PEDV) infection was demonstrated in 7 swine farms employing continuous pig flow management even after seasonal outbreaks. Clinically, sporadic postweaning diarrhea was a major concern in those farms. Subsequently circulatory antibody detection using serum neutralizing test made useful for confirmation of PEDV persistent infections. The persistence of PEDV in the premise might have induced recurrence over the period of time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.1-16
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• 2010

An epidemic model with Classical Kermack-Mckendrick incidence rate under a limited resource for treatment is proposed to understand the effect of the capacity for treatment. We have assumed that treatment function is strictly increasing function of infective individuals and becomes constant when the number of infective is very large. Existence and stability of the disease free and endemic equilibrium are investigated, boundedness of the solutions are shown. Even in this simple version of the model, backward bifurcation and multiple epidemic steady states can be observed with some sets of parameter values. Hopf-bifurcation analyses are given and numerical examples are provided to help understanding.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.11
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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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• v.17 no.1
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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.