Daşbaşı Bahatdin
Kayseri University, Faculty of Applied Sciences, TR-38039 Kayseri, Turkey.
Comput Math Methods Med. 2018 Dec 4;2018:7930603. doi: 10.1155/2018/7930603. eCollection 2018.
In this study, the mathematical model examined the dynamics between pathogen and specific immune system cells (memory T cells) for diseases such as chronic infection and cancer in which nonspecific immune system cells are inadequate to destroy the pathogen and has been suggested by using a system of the fractional-order differential equation with multi-orders. Qualitative analysis of the proposed model reveals the equilibrium points giving important ideas about the proliferation of the pathogen and memory T cells. According to the results of this analysis, the possible scenarios are as follows: the absence of both pathogen and memory T cells, only the existence of pathogen, and the existence of both pathogen and memory T cells. The qualitative analysis of the proposed model has expressed the persistent situations of the disease where the memory T cells either do not be able to respond to the pathogen or continue to exist with the disease-causing pathogen in the host. Results of this analysis are supported by numerical simulations. In the simulations, the time-dependent size of the tumor population under the pressure of the memory T cells was tried to be estimated.
在本研究中，该数学模型通过一个多阶分数阶微分方程组，研究了诸如慢性感染和癌症等疾病中病原体与特定免疫系统细胞（记忆T细胞）之间的动态关系，在这些疾病中，非特异性免疫系统细胞不足以消灭病原体。对所提出模型的定性分析揭示了平衡点，这为病原体和记忆T细胞的增殖提供了重要信息。根据该分析结果，可能出现的情况如下：病原体和记忆T细胞均不存在、仅存在病原体、病原体和记忆T细胞均存在。对所提出模型的定性分析表明了疾病的持续情况，即记忆T细胞要么无法对病原体作出反应，要么与致病病原体在宿主体内持续共存。该分析结果得到了数值模拟的支持。在模拟中，尝试估计在记忆T细胞压力下肿瘤群体随时间变化的大小。
