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A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea. (English) Zbl 1397.92690
Summary: We have developed a dynamic model for tuberculosis (TB) transmission in South Korea using a SEIR model with the time-dependent parameters. South Korea ranked the highest TB incidence among members of the Organization for Economic Cooperation and Development (OECD) in 2005 yr. The observed data from the Korea Center for Disease Control and Prevention (KCDC) shows a certain rise of active-TB incidence individuals after 2001 yr. Because of this sudden jump, we have considered two different periods for best fitting the model: prior to 2001 yr and posterior to 2001 yr. The least-squares fitting has been used for estimating model parameters to the observed data of active-TB incidence. Our model agrees well with the observed data. In this work, we also propose optimal treatment strategies of TB model in South Korea for the future. We have considered three control mechanisms representing distancing, case finding and case holding efforts. Optimal control programs have been proposed in various scenarios, in order to minimize the number of exposed and infectious individuals and the cost of implementing the control treatment.

MSC:
92D30 Epidemiology
92C60 Medical epidemiology
49N90 Applications of optimal control and differential games
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