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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

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带有免疫治疗的离散流脑模型的动力学性态（英）

马   霞1,   曹   慧2,   张晋珠1,   郭尊光1   

  1. 1- 太原工业学院理学系，太原  030008 2- 陕西科技大学理学院，西安  710021
  • 收稿日期:2019-01-23 接受日期:2019-10-24 出版日期:2021-06-15 发布日期:2021-08-15
  • 基金资助:
    山西省教育厅自然科学基金 (201901D111322)；太原工业学院后备学科带头人项目 (2018008).

Threshold Dynamics of Discrete Meningococcal Meningitis Model with Vaccination and Therapy

MA Xia1,   CAO Hui2,   ZHANG Jin-zhu1,   GUO Zun-guang1   

  1. 1- Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
    2- College of Science, Shaanxi University of Science and Technology, Xi'an 710021
  • Received:2019-01-23 Accepted:2019-10-24 Online:2021-06-15 Published:2021-08-15
  • Supported by:
    The Natural Science Foundation of Department of Education of Shanxi Province (201901D111322); the Reserved Discipline Leaders of Taiyuan Institute of Technology (2018008).

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摘要： 根据流脑在我国的流行特点和疫苗因素的影响，文中采用隐式欧拉法建立了一类带有免疫治疗的离散SCIRS模型，并研究了模型的全局动力学特性．通过构造合适的Lyapunov函数得到了模型平衡点全局稳定的充分条件，利用动力系统的持久性理论进一步得出了疾病的持久性．最后，利用数值模拟对理论结果进行了验证与推广．

关键词: 离散流脑模型, 隐式欧拉法, 持续性, 全局渐近稳定, Lyapunov函数, 数值模拟

Abstract: According to the epidemic characteristics of Meningococcal Meningitis in China and the influence of vaccination factors, we formulate a discrete-time SCIRS model with vaccination and therapy by using the backward Euler method and investigate its dynamic characteristics. We obtain sufficient conditions for the global behavior of the equilibrium points by constructing suitable Lyapunov functions. We further conclude that the disease is permanent by using the theory of persistence in dynamical systems.~Numerical simulations are carried out to illustrate the main theoretical results.

Key words: discrete Meningococcal Meningitis model, backward Euler, persistent, globally asymptotically stability, Lyapunov function, numerical simulation

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