在线咨询
中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (2): 229-244.doi: 10.3969/j.issn.1005-3085.2026.02.002cstr: 32411.14.cjem.CN61-1269/O1.2026.02.002

• • 上一篇    下一篇

具有肝脏–病毒–血液传播的HBV感染模型的稳定性和最优控制研究

刘利利1,  马晓敏1,  覃文杰2   

  1. 1. 山西大学复杂系统研究所，太原  030006

    2. 云南民族大学数学与计算机科学学院，昆明 650031

  • 收稿日期:2023-06-19 接受日期:2023-12-15 出版日期:2026-04-15 发布日期:2026-06-15
  • 通讯作者: 覃文杰 E-mail: wenjieqin@hotmail.com
  • 基金资助:
    国家自然科学基金 (12126349; 12261104)；山西省自然科学基金 (202303021211003)；云南省“兴滇英才支持计划”青年人才专项 (XDYC-QNRC-2022-0708)；云南省基础研究专项 (202301AT070016).

Stability and Optimal Control of HBV Infection Model with Liver-Virus-Blood Transmission

LIU Lili1,  MA Xiaomin1,  QIN Wenjie2   

  1. 1. Complex System Research Center, Shanxi University, Taiyuan 030006
    2. Department of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031
  • Received:2023-06-19 Accepted:2023-12-15 Online:2026-04-15 Published:2026-06-15
  • Contact: W. Qin. E-mail address: wenjieqin@hotmail.com
  • Supported by:
    The National Natural Science Foundation of China (12126349; 12261104); the Natural Science Foundation of Shanxi Province (202303021211003); the Youth Talent of Xingdian Talent Support Program (XDYC-QNRC-2022-0708); the Basic Research Program Project of Yunnan Province (202301AT070016).

摘要：

为有效预防和控制HBV感染，建立了基于病毒在肝脏及血液传播的HBV感染模型。利用Routh-Hurwitz判据、Lyapunov-LaSalle不变集原理等相关理论证明了模型基于基本再生数的阈值动力学行为。进一步，引入两种抗病毒治疗的控制措施，干扰素治疗和核苷(酸)类治疗，研究了其对应的优化控制问题，利用庞特里亚金极小值原理证明了最优控制策略的存在唯一性。最后，通过向前-向后扫描法进行数值模拟，讨论了血液传播以及优化控制对HBV感染模型的影响。研究结果表明，忽略血液传播会低估HBV在人体内的传播水平，优化控制策略可明显提高健康细胞的浓度、降低病毒载量，同时核苷(酸)类药物的疗效要优于干扰素药物的治疗效果。

关键词: HBV感染模型, 血液传播, 稳定性, 抗病毒治疗, 优化控制

Abstract:

To effectively prevent and control HBV infection, a HBV infection model with liver-virus-blood transmission is developed in this paper. By employing the Routh-Hurwitz criterion, Lyapunov-LaSalle invariant set principle and other related theories, it is proven that the threshold dynamic behavior of the model is determined by the basic reproductive number. Furthermore, two control measures of antiviral therapy, interferon therapy and nucleoside (acid) therapy, are introduced to study the corresponding optimal control problem, and the existence and uniqueness of the optimal control strategy are proved by Pontriagin's minimum principle. Finally, the influence of blood transmission and optimal control on HBV infection model is discussed by forward-backward sweeping method to simulate. The results show that ignoring blood transmission will underestimate the level of HBV infection, and the optimal control strategy can significantly improve the concentration of healthy cells and reduce the viral load. Meanwhile, the therapy effect of nucleotide (acid) is better than that using interferons.

Key words: HBV infection model, blood transmission, stability, antiviral therapy, optimal control

中图分类号: