一类糖尿病模型的动力学行为及敏感性分析

李畅通; 田佳; 冯孝周; 刘云涛

doi:10.21656/1000-0887.460021

一类糖尿病模型的动力学行为及敏感性分析

doi: 10.21656/1000-0887.460021

西安工业大学基础学院，西安 710021

基金项目:

陕西省哲学社会科学研究专项 2025YB0201

陕西省外国专家服务计划项目 2024WZ-YBXM-01

国家自然科学基金 12326417

国家外专项目 G2023041033L

详细信息

作者简介:
田佳(2003—)，女，硕士生(E-mail: 15229924801@163.com)

冯孝周(1979—)，男，教授，博士，博士生导师(E-mail: flxzfxz8@163.com)

刘云涛(2000—)，男，硕士生(E-mail: liyto22@163.com)

通讯作者:
李畅通(1982—)，男，副教授，博士(通信作者. E-mail: lctnihao@163.com)

中图分类号: O175.1
计量
- 文章访问数: 22
- HTML全文浏览量: 14
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2025-02-06
- 修回日期: 2025-05-12
- 刊出日期: 2026-02-01

Dynamic Behavior and Sensitivity Analysis on a Class of Diabetes Models

School of Sciences, Xi'an Technological University, Xi'an 710021, P.R.China

摘要

摘要: 基于糖皮质激素诱导胰岛素抵抗，建立了一类新的胰岛素、血糖和糖皮质激素的糖尿病模型，探究了糖尿病的复杂发病机制. 首先，运用线性化方法、极限系统理论以及Dulac判据，证明了平衡点的局部和全局稳定性. 其次，选取了影响糖尿病浓度的关键参数，通过直接微分法，开展了关键参数对正平衡点的敏感性分析，探究了关键参数如何影响胰岛素和糖皮质激素的分泌与作用，进而帮助调控血糖水平的波动. 最后，运用MATLAB进行数值模拟，不仅验证了理论分析的正确性，还模拟了不同干预治疗下血糖浓度的变化趋势，发现选取合适的关键参数对血糖浓度的控制至关重要，为糖尿病临床治疗方案的制定提供了理论依据.
- 糖尿病模型 /
- 稳定性 /
- Dulac判据 /
- 敏感性分析
Abstract: Based on the fact that glucocorticoid induces insulin resistance, a new type of diabetes model involving insulin, glucose, and glucocorticoid was established to explore the complex pathogenesis of diabetes. Firstly, the local and global stability of the equilibrium point was demonstrated with the linearization method, the limit system theory, and the Dulac criterion. Secondly, the key parameters affecting glucose concentration were selected, and the sensitivity analysis of the key parameters with respect to the positive equilibrium point was carried out with the direct differentiation method. This analysis shows how the key parameters influence the secretion and function of insulin and glucocorticoid, thereby helping to regulate the fluctuations of glucose levels. Finally, numerical simulations were conducted on MATLAB. These simulations not only verify the correctness of the theoretical analysis, but also reveal the changing trends of glucose concentrations under different intervention treatments. The results indicate that, the selection of appropriate key parameters is crucial for the control of glucose concentration, which provides a theoretical basis for formulating clinical treatment plans for diabetes.
- diabetes model /
- stability /
- Dulac criterion /
- sensitivity analysis

HTML全文

图 1 糖尿病模型系统图

Figure 1. System diagram of the diabetes model

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图 2 当参数τ₀＜1时的数值模拟结果

Figure 2. Numerical simulation results with parameter τ₀ < 1

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图 3 当参数τ₀＜1时，不同初始值的数值模拟图

Figure 3. Numerical simulation plots of different initial values for parameter τ₀ < 1

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图 4 当参数τ₀>1时的数值模拟结果

Figure 4. Numerical simulation results with parameter τ₀>1

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图 5 当参数τ₀>1时，不同初始值的数值模拟图

Figure 5. Numerical simulation plots of different initial values for parameter τ₀>1

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图 6 参数σ₁, m, c, ω与I^*, G^*, H^*之间的影响关系

Figure 6. The relationships between parameters σ₁, m, c, ω and I^*, G^*, H^*

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