具时滞慢性粒细胞白血病免疫模型的稳定性与分支  

Stability and Bifurcation of the Immune Model of Chronic Myeloid Leukemia with Time Delay

作　　者：王晶囡 孙悦 WANG Jingnan;SUN Yue(School of Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2024年第5期132-141,共10页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11801122);黑龙江省自然科学基金(A2018008)。

摘　　要：为了研究慢性粒细胞白血病干细胞分化时滞对白血病干细胞,白血病成熟细胞和效应T细胞之间的动力学行为影响,建立了带有干扰素-α和伊马替尼治疗项的慢性粒细胞白血病免疫时滞模型。通过对改进的时滞模型稳定性分析,依据规范型和中心流形理论,得到Hopf分支的临界条件与性质。并给出干扰素-α和伊马替尼联合效应T细胞控制慢性粒细胞白血病的条件,如在药物干预下,调节分化时滞会使慢性粒细胞白血病干细胞与白血病成熟细胞的数量呈现稳定不增状态,或由大振幅周期波动转向为小振幅波动状态。最后,数值模拟验证了所得理论。In order to investigate the effects of the differentiation delay in chronic myeloid leukemia stem cells on the dynamic behaviors among chronic myeloid leukemia stem cells,chronic myeloid leukemia mature cells and effector T cells,a delayed immune model of chronic myeloid leukemia with the treatment of interferon-alpha and imatinib is established.Through the stability analysis of the modified time-delay model,using normal form and central manifold theory,the critical conditions and properties of Hopf bifurcation are obtained.In addition,the conditions for the control of chronic myeloid leukemia by interferon-alpha and imatinib combined with effector T cells are given.For example,under the intervention of drugs,adjusting the time delay of differentiation can make the number of stem cells and mature cells of chronic myeloid leukemia show a stable and non-increasing state,or transition from large amplitude periodic oscillation state to small periodic oscillation state.Finally,numerical simulations verify the obtained theories.

关 键 词：慢性粒细胞白血病 稳定性 HOPF分支 周期解 细胞分化时滞 

分 类 号：O175[理学—数学] O193[理学—基础数学]