ABSTRACT

Since mathematical models play a key role in investigating the dynamics of infectious diseases, many mathematical models for these diseases are developed. In this paper, it is aimed to determine the dynamics of Tuberculosis (TB) in Turkey, how much it will affect the future and the impact of vaccine therapy on the disease. For this purpose, three mathematical models (SIR, SEIR and BSEIR) in the literature are considered for the case of Turkey. The model parameters are obtained with TB reported data from 2005 to 2015 by using the least square method. The obtained results revealed that the basic reproduction ratio for all three models is less than 1. Moreover, the stability analysis of the models and sensitivity analysis of the model parameters are presented and discussed. Finally, the accuracy of results for all three models is compared and the effect of the vaccination rate is discussed.

摘要

由于数学模型在研究传染病的动态中起关键作用，因此开发了许多针对这些疾病的数学模型。本文旨在确定土耳其结核病（TB）的动态，对未来的影响以及疫苗治疗对该疾病的影响。为此，考虑了土耳其的三种数学模型（SIR，SEIR和BSEIR）。模型参数是使用最小二乘法从2005年至2015年的结核病报告数据中获得的。获得的结果表明，所有三个模型的基本再现率均小于1。此外，对模型的稳定性分析和模型参数的敏感性分析进行了介绍和讨论。最后，