• Communications of Mathematical Education
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• v.24 no.4
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• pp.877-889
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• 2010

Mathematical modelling is a useful method for reinterpreting the real world and for solving real problems. In this paper, we introduced a theory on mathematical modelling. Further, we developed a mathematical model of the H1N1 influenza with Excel. Then, we analyzed the model which tells us what role it can play in an appropriate prediction of the future and in the decision of accompanied policies.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.597-608
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• 2007

We present a general uniqueness result of an endemic state for an S-I-R model with external force of infection. We reduce the problem of finding non-trivial steady state solutions to that of finding zeros of a real function of one variable so that we can easily prove the uniqueness of an endemic state. We introduce an assumption which was usually used to show stability of a non-trivial steady state. It turns out that such an assumption adopted from a stability analysis is crucial for proving the uniqueness as well, and the assumption holds for almost all cases in our model.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.651-659
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• 2012

In this paper we developed a statistical model for circular data with noises. In this case, model fitting by single circular model has a lack-of-fit problem. To overcome this problem, we consider some mixture models that include circular uniform distribution and apply an EM algorithm to estimate the parameters. Both von Mises and Wrapped skew normal distributions are considered in this paper. Simulation studies are executed to assess the suggested EM algorithms. Finally, we applied the suggested method to fit 2008 EHFRS(Epidemic Hemorrhagic Fever with Renal Syndrome) data provided by the KCDC(Korea Centers for Disease Control and Prevention).

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.641-650
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• 2012

Spatial time series data can be viewed as a set of time series simultaneously collected at a number of spatial locations. This paper studies Bayesian inferences in a spatial time bilinear model with a Gibbs sampling algorithm to overcome problems in the numerical analysis techniques of a spatial time series model. For illustration, the data set of mumps cases reported from the Korea Center for Disease Control and Prevention monthly over the years 2001~2009 are selected for analysis.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.699-702
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• 1998

This study investigates the population model of the spread of HIV/AIDS which the infection is generated by an infectious in dividual in a population of susceptibles. A mathematical model is presented for the transmission dynamics of HIV infection within the communities of homosexual males. The pattern on the epidemic character of HIV, the causative agent of AIDS, was analysed by the mathematical model of AIDS system which is derived according to the ecological relationship between five epidemilogic states of individuals. The computer simulation was performed using real data.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.685-699
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• 2019

This research is focused on a continuous epidemic model of transmission of Plasmodium vivax malaria with a time delay. The model is represented as a system of ordinary differential equations with delay. There are two equilibria, which are the disease-free state and the endemic equilibrium, depending on the basic reproduction number, $R_0$, which is calculated and decreases with the time delay. Moreover, the disease-free equilibrium is locally asymptotically stable if $R_0<1$. If $R_0>1$, a unique endemic steady state exists and is locally stable. Furthermore, Hopf bifurcation is applied to determine the conditions for periodic solutions.

• Journal of Veterinary Science
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• v.24 no.2
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• pp.21.1-21.5
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• 2023

Under the current African swine fever (ASF) epidemic situation, a science-based ASF-control strategy is required. An ASF transmission mechanistic model can be used to understand the disease transmission dynamics among susceptible epidemiological units and evaluate the effectiveness of an ASF-control strategy by simulating disease spread results with different control options. The force of infection, which is the probability that a susceptible epidemiological unit becomes infected, could be estimated by applying an ASF transmission mechanistic model. The government needs to plan an ASF-control strategy based on an ASF transmission mechanistic model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.281-295
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• 2023

This study aims to establish and analyze a mathematical model for the transmission dynamics of male adolescent smoking and to determine an optimal control strategy to reduce male adolescent smoking. We consider three groups in the population: smokers, non-smokers, and temporary nonsmokers. In our model to which optimal control theory was applied, the number of smokers decreased sharply and the number of non-smokers increased significantly. Our simulation results under various control scenarios reveal that integrated control measures(such as prevention, education, and treatment) may be necessary to reduce the growth rate of adolescent smoking. Moreover, we concluded that efforts to encourage current smokers and temporary quitters to quit should be sustained longer than efforts to reduce the rate at which nonsmokers become smokers through smoking prevention education.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1393-1407
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• 2023

In this study, we propose a dynamic SEIQRV mathematical model and examine it to comprehend the dynamics of COVID-19 pandemic transmission in the Coimbatore district of Tamil Nadu. Positiveness and boundedness, which are the fundamental principles of this model, have been examined and found to be reliable. The reproduction number was calculated in order to predict whether the disease would spread further. Existing arrangements of infection-free, steady states are asymptotically stable both locally and globally when R₀ < 1. The consistent state arrangements that are present in diseases are also locally steady when R₀ < 1 and globally steady when R₀ > 1. Finally, the numerical data confirms our theoretical study.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.711-738
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• 2024

This study develops an optimal control strategy for canine rabies transmission using a two-dimensional spatiotemporal model with spatial dynamics. Our objective is to minimize the number of infected and exposed individuals while reducing vaccination costs. We rigorously establish the existence of optimal control and provide a detailed characterization. Numerical simulations show that early intervention, in particular timely vaccination at the onset of an outbreak, effectively controls the disease. Our model highlights the importance of spatial factors in rabies spread and underlines the need for proactive vaccination campaigns, providing valuable insights for public health policy and intervention strategies.