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Cho, Giphil,Jeong, Yong Dam,Kim, Sangil,Jung, Il Hyo The Youngnam Mathematical Society 2018 East Asian mathematical journal Vol.34 No.5
We consider an optimal control problem for an impulsive stage-structured model involving ordinary differential equations with impulsive values of initial conditions in the next year. The main goal is to maximize a profit of the catch of Pacific cod in the South Korea through optimal harvest strategy as a control of adult cod. We established necessary conditions for the optimal harvest control using idea of Pontryagin's maximum principle. The optimal harvest strategy is to numerically solve the equation by using an iterative method with the Runge-Kutta method. Finally, we compare a monthly average of fishing mortality of Pacific cod from 2013 to 2017 with monthly fishing mortality for result obtained optimal harvest strategy.
State-Dependent Impulsive Control Strategies for a Tumor-Immune Model
Kim, Kwang Su,Cho, Giphil,Nie, Lin-Fei,Jung, Il Hyo Hindawi Limited 2016 Discrete dynamics in nature and society Vol.2016 No.-
<P>Controlling the number of tumor cells leads us to expect more efficient strategies for treatment of tumor. Towards this goal, a tumor-immune model with state-dependent impulsive treatments is established. This model may give an efficient treatment schedule to control tumor’s abnormal growth. By using the Poincaré map and analogue of Poincaré criterion, some conditions for the existence and stability of a positive order-1 periodic solution of this model are obtained. Moreover, we carry out numerical simulations to illustrate the feasibility of our main results and compare fixed-time impulsive treatment effects with state-dependent impulsive treatment effects. The results of our simulations say that, in determining optimal treatment timing, the model with state-dependent impulsive control is more efficient than that with fixed-time impulsive control.</P>
Optimal Treatment Strategy for a Tumor Model under Immune Suppression
Kim, Kwang Su,Cho, Giphil,Jung, Il Hyo Hindawi Publishing Corporation 2014 Computational and mathematical methods in medicine Vol.2014 No.-
<P>We propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8<SUP>+</SUP>T-cells, CD4<SUP>+</SUP>T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer.</P>
Analysis of a vector-bias effect in the spread of malaria between two different incidence areas
Kim, Sungchan,Masud, M.A.,Cho, Giphil,Jung, Il Hyo Elsevier 2017 Journal of theoretical biology Vol.419 No.-
<P><B>Abstract</B></P> <P>In 2005, Lacroix et al. demonstrated that infected humans are more attractive to mosquitoes, a phenomenon known as the vector-bias effect. The aim of this study was to determine how a vector-bias effect affects the changes in the dynamics of malaria transmission, and the changes in control strategies and cost-effectiveness for optimal control considering the regional characteristics or force of infections for different transmission rates. We used a vector-bias mathematical model and considered two different incidence areas: a high transmission area and a low transmission area. Our results showed that the dynamics in the two areas differed; as bias exists and the strategy for optimal control could be changed in the different areas. Thus, this work may give that considering the vector-bias effect in different areas facilitates prediction of the future dynamics and make decisions for establishing controls. We also mention the evolution of malaria parasites in this study.</P>