强随机扰动下溶瘤病毒疗法的动力学分析
Dynamics Analysis of Oncolytic Virus Therapy under Strong Stochastic Perturbations
DOI: 10.12677/aam.2026.156291, PDF,   
作者: 张钫涯：兰州理工大学理学院，甘肃 兰州
关键词: 随机扰动；阈值；灭绝与持久；Stochastic Perturbation； Threshold； Extinction and Persistence
摘要: 溶瘤病毒疗法是一种新兴的癌症治疗方法。本文考虑随机扰动对溶瘤病毒疗法的影响，提出了描述健康的肿瘤细胞和被溶瘤病毒感染的肿瘤细胞间相互作用的随机模型，证明了该模型全局正解的存在唯一性和矩的有界性，并对模型的边界系统进行了分析。最后给出了该模型在强σ1随机扰动下的阈值λ2，通过阈值对模型的动力学行为进行了分析。研究发现随机扰动会抑制肿瘤细胞的生长，在溶瘤病毒疗法治疗癌症的过程中随机扰动的影响不容忽视。
Abstract: Oncolytic virotherapy is an emerging approach for cancer treatment. This paper considers the influence of stochastic perturbations on oncolytic virotherapy, and proposes a stochastic model to describe the interaction between uninfected tumor cells and oncolytic virus-infected tumor cells. The existence and uniqueness of global positive solutions and moment boundedness of the model are proved, and the boundary system of the model is analyzed. Finally, the threshold value λ2 of the model under strong stochastic perturbation σ1 is derived, and the dynamical behaviors of the model are analyzed based on this threshold. The research results show that stochastic perturbations can inhibit the growth of tumor cells, and their effects cannot be neglected in the treatment of cancer with oncolytic virotherapy.
文章引用：张钫涯. 强随机扰动下溶瘤病毒疗法的动力学分析[J]. 应用数学进展, 2026, 15(6): 337-346. https://doi.org/10.12677/aam.2026.156291

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